parametric_via_three_wave_mixing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Parametric Pumping via Three-Wave Mixing"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using HarmonicBalance, Plots\n",
    "using Plots.Measures\n",
    "using Random"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "## System"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "System of 1 differential equations\nVariables:       x(t)\nHarmonic ansatz: x(t) => ω;   \n\nDifferential(t)(Differential(t)(x(t))) + Differential(t)(x(t))*γ + (x(t)^2)*β + x(t)*(ω0^2) + (x(t)^3)*α ~ F*cos(t*ω)\n"
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "cell_type": "code",
   "source": [
    "@variables β α ω ω0 F γ t x(t) # declare constant variables and a function x(t)\n",
    "diff_eq = DifferentialEquation(\n",
    "    d(x, t, 2) + ω0^2 * x + β * x^2 + α * x^3 + γ * d(x, t) ~ F * cos(ω * t), x\n",
    ")\n",
    "add_harmonic!(diff_eq, x, ω) # specify the ansatz x = u(T) cos(ωt) + v(T) sin(ωt)"
   ],
   "metadata": {},
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 1st order Krylov expansion"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "2-element Vector{Symbolics.Equation}:\n (-(1//2)*u1(T)*γ*ω + (1//2)*v1(T)*(ω^2) - (1//2)*v1(T)*(ω0^2) - (3//8)*(u1(T)^2)*v1(T)*α - (3//8)*(v1(T)^3)*α) / ω ~ Differential(T)(u1(T))\n (-(1//2)*F - (1//2)*u1(T)*(ω^2) + (1//2)*u1(T)*(ω0^2) - (1//2)*v1(T)*γ*ω + (3//8)*(u1(T)^3)*α + (3//8)*u1(T)*(v1(T)^2)*α) / ω ~ Differential(T)(v1(T))",
      "text/latex": "$$ \\begin{align}\n\\frac{ - \\frac{1}{2} \\mathrm{u1}\\left( T \\right) \\gamma \\omega + \\frac{1}{2} \\omega^{2} \\mathrm{v1}\\left( T \\right) - \\frac{1}{2} {\\omega}0^{2} \\mathrm{v1}\\left( T \\right) - \\frac{3}{8} \\left( \\mathrm{u1}\\left( T \\right) \\right)^{2} \\mathrm{v1}\\left( T \\right) \\alpha - \\frac{3}{8} \\left( \\mathrm{v1}\\left( T \\right) \\right)^{3} \\alpha}{\\omega} &= \\frac{\\mathrm{d} \\mathrm{u1}\\left( T \\right)}{\\mathrm{d}T} \\\\\n\\frac{ - \\frac{1}{2} F - \\frac{1}{2} \\omega^{2} \\mathrm{u1}\\left( T \\right) + \\frac{1}{2} {\\omega}0^{2} \\mathrm{u1}\\left( T \\right) - \\frac{1}{2} \\mathrm{v1}\\left( T \\right) \\gamma \\omega + \\frac{3}{8} \\left( \\mathrm{u1}\\left( T \\right) \\right)^{3} \\alpha + \\frac{3}{8} \\left( \\mathrm{v1}\\left( T \\right) \\right)^{2} \\mathrm{u1}\\left( T \\right) \\alpha}{\\omega} &= \\frac{\\mathrm{d} \\mathrm{v1}\\left( T \\right)}{\\mathrm{d}T}\n\\end{align}\n $$"
     },
     "metadata": {},
     "execution_count": 3
    }
   ],
   "cell_type": "code",
   "source": [
    "harmonic_eq = get_krylov_equations(diff_eq; order=1)\n",
    "harmonic_eq.equations"
   ],
   "metadata": {},
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "source": [
    "If we both have quadratic and cubic nonlineariy, we observe the normal duffing oscillator response."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=3}",
      "image/png": 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",
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      ]
     },
     "metadata": {},
     "execution_count": 4
    }
   ],
   "cell_type": "code",
   "source": [
    "varied = (ω => range(0.99, 1.1, 200)) # range of parameter values\n",
    "fixed = (α => 1.0, β => 1.0, ω0 => 1.0, γ => 0.005, F => 0.0025) # fixed parameters\n",
    "\n",
    "result = get_steady_states(harmonic_eq, varied, fixed; threading=true)\n",
    "plot(result; y=\"u1^2+v1^2\")"
   ],
   "metadata": {},
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "source": [
    "If we set the cubic nonlinearity to zero, we recover the driven damped harmonic oscillator. Indeed, thefirst order the quadratic nonlinearity has no affect on the system."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=1}",
      "image/png": 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",
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fcbmEXqzHyFhsAwAgOR518DnO4vFsnr16sTERLlcPnr06PoXnD9/ftOmTXPnzmUPf/31171793bu3Dk/P79r165DhgwRqWCB82ceISbUAwBIlVg1wkceeWTYsGFjx47Nz8/fsGFDnbMrV67cuHHjunXrXM+cPXt29+7d77//vtPpvPnmm0UqVeDsPNmcpJCRRu7V9dXzCKvQRwgAIFGi1AiNRuPhw4dTU1OJaNiwYQ888MCECRNqXzB9+vQTJ06sX7++9pOrV6/WarVilCeIjL4MGSXUCAEAJE+UIDx58qRKpWLH0dHRR48e9eanjhw5UlZWJghCenp6Y9cIgmC1WktLS9lDvV6vVHodSsHg00KjhHmEAACSJ0oQlpWVuep2UVFR5eXlPM/LZO6aYVNTU6OjowcPHvzf//739ddf/+c//9ngZSdOnFi1atWXX37JHj755JPz5s0LbuHdu1rBEami5LzJZKpzymKxqFQqufxPbaZyO0ekKrc1cH1kMpvNHOftnxGRCbfII57nrVarIKDHwR0vv0hqtbqJqxMS9KcgzMvL++qrrxITE6dOnapSqfbt23f16tXbbrstJibGpxfV6XQWi4UdWywWjUbjPgWJaPDgwexg+PDh/fr1aywIe/bs+dhjjy1YsMCn8gSRs1IgcsSoZXq9vs4puVxePwhbyonIXunk6l8fmQRBwK1wD7fII57n5XK5TqcLdUEkDV8k713Lp/Ly8nHjxp09e/brr78eM2ZMRUXFzTffvHr16p9//tnXF01OTq6oqGDHRqMxOTnZ44/069fv3LlzRKRQKMxms9Pp9PVNm4ZPQ0YJfYQAAJJ3rUa4Y8eO1atXX3fddUR04sSJF1544a233oqOjvbjRdu3b9+6dWubzaZWq8+dOzd+/Hgiunz58rZt2x566CF2jdPprJ12EydOZINrsrKy0tPT69SrpMOnhUaJKEpBChlZHOTgSYFJmwAA0nMtCKOjoxMSEqxWq0aj6dGjx/z585ctW+Zw+FmX+fe///3RRx917tx53759zz33HBGVl5efPn2and20aVNGRkZsbOy7776bnp7esWPHO+64Y+XKlYIgHD16dMmSJYF/MJH4tNAoo1NQeRWZHBSrEqlQAADgv2tBOGLEiOXLl8+fP/+LL74YMmRIdHT07NmzMzMz/XvdPn369OnTh4jGjBnDnunVq9fChQvZ8bhx48aNG1f7+p49e/bs2ZOI7r33Xv/esWn4tNAoo1dy5VWCyS7EqjACAgBAcq79RpfJZA888MD06dNdAz5VKlUglcJmydd5hIRV1gAApK1ut1WdKe0cxzU2sjYvL0+sQkkY20dC50sQYt1tAAAp83/8xgcffBDEcoSLmhqhD42cGDgKACBljXZ2CYJw8eLFxqasOhwO18iXiGLyZQ8mpmZxGYEIfYQAAJLTaBDa7fbRo0efOnWqsQu6d+8uTpEkzY/BMtFKjkhA0ygAgDQ1+htdpVK9+OKLKSkpPXr0qH/Wbre7dlCKKP4MlsFyowAAEuauatO3b9+9e/c2tjVgx44dxSmSpJl8nFBPGDUKACBt7oKwU6dOUVFR7NhsNms0mtoLvjz11FPiFk2SWI3Q4MvUeIwaBQCQMndBqFAo2rdvT0S7d+/+y1/+0r9//zvuuMNgMIwZMyYtLS0uLq6pCikhpVVERHE+BaGKo5q12QAAQGq8GvXRv3//lStXTp48WSaTOZ3OrVu3btu27f7775f+PrpBV2ITiChe7UPTKEvNsiqRSgQAAAHxah6hXq+/66672FZKcrl83LhxM2fOXL58uchlkxxeoPIqknEU40uNME5NRFRqE6lQAAAQEG8n1P/000/79u3jeZ491Ol0cXFxrk0HI0R5FfECxahI5suEwDg1R0SlNjSNAgBIkVdNozt37vzwww+PHDlit9vvvPPOW2+9NS4ubvPmzVOnThW7fJJSWiUQUZyPa2ezptES1AgBACTJqyBUqVRvvPFGly5dMjMzV69evXjxYo7jXnzxRY6LrKVSWPMma+r0XjxrGkUfIQCAJHkVhEOHDl21atWOHTtmzJjx9ttvi10myfIvCNE0CgAgZd6uFTZt2jSr1RppVcA62JBRX5tGo5WklJHRTnaelNikHgBAYnz4xazRaNRqH2tDzUv1JELf70EMZlAAAEgVaig+YE2j8b4HYTxaRwEApMqXbRQiHkuyOF9m0zOYSggAzUZmZuZbb70V6lJ46/bbb58zZ477axCEPvBjfTWG/QgGjgJAM3D48OHS0lKP6SIFBw8e3LZtG4IwmPwbNUrVlUihxIa9eQGgOejQocPkyZNDXQrPlErlmTNnPF7mWx9hZO5K7+J302g8mkYBAKTKtyDcv3+/SOUIC2x1GH+aRhGEAABShVGjPvB7+gSbeshWaAMAAElBEPqg1Pc9mBjUCAEAJAtB6C2nQEY7ybnqHed9woIQ624DAEiQh1GjFy9eLC4urv3w0KFDtS/o2bNnhCw3w/Zgilf7tgcTU900ign1AADS46FGyDbjbQzHcZGz+qjfQ0YJG1AAAIgsOzvb75/1UCNMSUlJSUlxPczKyrrhhhv8frOw5veQUUIfIQCAaFasWJGVlXX48OHvv//ev1dAH6G3/B4yStiJCQBANHffffekSZMCeQWsLOMtv4eMEpFOQWo5mR1kc5JaHuySAQCE1FUL5Zib6A/9eDWlRQe5Sw5B6C2/11djYlVUYKGyKkrSBrFQAACh12e9Pd/SRO8l5+jEJEWXmGBmoW9BOGTIkCC+d3jxe8VtJk7NFViEUpuQpI2U4UUAECEmpcn2X22iGmGKnmsdFdIaYceOHYP79mEkkFGjVJOgmEoIAM3Pe4PDu8sHg2W8FWDTaBxmUAAASBKC0FuBTJ8gbFIPACCO/fv3r1mz5tSpU2vXri0sLPTjFRCE3gq0aRRTCQEARNCxY8dnn3326NGjw4YN0+l0frwCRo16i7VqxvvdNIpN6gEARNCyZcsAXwE1Qm8F3EeIplEAACmqG4Qmk6mqqrraUllZ2eTlka6gNI1i1CgAgNT8KQgfeeSRhISExMTEpUuXEtGpU6dGjx79888/h6hsEhLIHkxMPPoIAQAk6VoQZmRkXHfddZWVldnZ2WfOnFmyZEnfvn3btGlTXl4ewvJJRKmNBKJYFfk9jROb1AMASNO1IMzLy5s7d65cLm/Tps2bb77ZsWPHrVu3yuXhPU0yWAJsFyWMGgUAkKprQXjrrbdu2LDhpZdeOn36NBHdfvvt7dq1Y8cQ4JBRutZHiBohAIC0XJs+0apVqwEDBly5ciU2NpY907t372XLlkXO1rtuBDhklK5NqA9SgQAAQkQul2/ZsmXEiBGhLohnhYWF3qwM+qd5hMnJyX//+99rPxPJi4vWFnjTqEZOGjlZnWR1kgbtzQAQtu6666727duHuhTe6tatm8dr/J9Qv2TJkoceesjvHw8vAW49wcSp6UolldqodVRQCgUAEAJ6vf72228PdSmCyf8J9VlZWUEsh8SVBNw0SjUDR9FNCAAgKY3WCG0228SJE12T6+twOBylpaWilUpyAm8aJaJ4DXupoJQIAACCo9EgVKvV/fr1czgcrrEztdnt9h07dohZMGkpDWzrCSZOxREJpVUC+T8dEQAAgsxdH+GYMWNycnKmTJnS4NmysjJxiiRFgU+fIEwlBACQJHd9hN26dXOzpcWoUaNEKI9EBaVpFMuNAgBIkLsaYWxsbHp6ev3nf/nlF5VK9Ze//EW0UklO4PMIybXKGgbLAABIiVejRvPz8+fNm/fVV1/l5+cT0cCBAzmOW7x4schlk5BgTZ8gbEkIACAxXgWhwWDQ6/XvvfdeSkpKjx49HnvssWPHjp06dcput4tdPokIzqhR9BECAEiPV0EYFRX12muv7du3r7S0dPHixbGxsW+//Xa/fv2UykY3Jfrjjz+WLl36zTffNDi41G637969+8MPP3Q9YzKZlixZsnnz5jVr1vjxMUTl4MlkJ4WM9P7uwcRgb14AAAnybUK9TqcbMWLE/Pnzjxw5YrVa3Vz54IMPzpgx44477sjMzNy3b1+ds5999tn+/fsPHjzoeubRRx8dPXr02LFjFQrF8uXLfSqV2EqrSCCKC2APJoa1rKJpFABAUrwKQqfT+f7773/yySd5eXnsGZVKlZiY2FgWHj9+XC6Xa7VaIhowYADb5re22bNn9+jRw/XQbDZnZmampKQQ0aBBgz7++GM/Pol4gtIuShg1CgAgSV6tNbpx48aioqJDhw498cQT/fr1Gzp0aHJy8s6dO6dNm9bg9b/99pter2fHer3++PHj7l//1KlTrlZW99c7nc7y8vLz58+zh0lJSW4meARLUIaM0rUNKNA0CgAgIV4FYadOneLi4l5++eXy8vJvv/32l19+KSgoeOGFFxrboam8vFyj0bDjqKgoj4uxlZeXq9Vq1/UWi8VqtbpeobZTp06tW7du586d7OHDDz/86KOPevMRApFXLiNSGuROk8lda7DFYlGpVG62MlbyRKQutZHJZAp+KcOE2WzGxl7u4RZ5xPO81WoVBPxN6Y6XXyS1Wu1mtEeE8CoIe/bsuWfPngULFsyYMePee++999573V8fHR1dWVnJjs1ms6t26OX1CoXClYt1dO/ePS4ubsGCBd4UO1gsMp7ImRil0Ovd1Qrlcrn7ICSiKIW90kGcRq/zf9uP8CYIgsfvQ4TDLfKI53m5XN4ErUFhDV8k73n7+/jWW2+99dZbvbw4NTW1oqKCHRuNRo87V6WkpLgqSUajMTU1VVJ/EQeraZSI4tRcpUMotQk6hYQ+IABAJPN/GyY3Bg8eXFlZyRousrOz77zzTiI6cODAp59+6rrGbre7piG2bNmyS5cuLDuzs7MnTpwoRqn8xoIwwIVGGUwlBACQGlFa6ORy+euvv/7pp58mJiZWVlY+8sgjRGS3212jTFeuXHno0CGlUvnBBx9MmTKlRYsWH3zwwfLlyzt37nzw4MEXX3xRjFL5rbRKoJoF0gKEGRQAAFIjVlfVzTfffPPNN9d+ZsiQIUOGDGHH06dPnz59eu2zHTt2nDt3LhGNHj1apCL5LbhNo0RCqQ07MQEASIUoTaPNTFCDkAhTCQEApARB6FkQm0bRRwgAIDUIQs+CWSNkOzFVYf4TAIBUIAg9Kwl20yhqhAAA0oEg9Kx6rdGgjBpFEAIASAyC0AM7T2YHKQPeg4lhaVqC5UYBACQDQegBq73FBrY3vQs2qQcAkBoEoQdXLAIRtYoKzrQ/NI0CAEgNgtCDyyaBiJKDtLpvKy1HRFcq0TQKACAVCEIPcs1ERMm64NQIY1RkUJLRTuVoHQUAkAYEoQe5ZoGI2gUpCF0vlWNGpRAAQBIQhB7kmIiI2gVv4zP2UqyiCQAAIYcg9IDVCJP1QasRspfKMaFGCAAgCQhCD3LMRKLUCBGEAACSgCD04I9KgYjaBmn6BF3rIwzW6wEAQEAQhO4UWcnioHh1cJaVYdgAVNQIAQAkAkHoTtCHjBJRsp4INUIAAMlAELrDJjkEazY9w2qEGCwDACARCEJ3cqtHygSzRhitJIOSzA4stAYAIAkIQnfEaBqlmhkU6CYEAJACBKE7bDY969ULIjaDAt2EAABSgCB0R6waIQaOAgBIBoLQnZzqFbeD/LLtEIQAAJKBIGyU4JpNH/w+QiI0jQIASAOCsFHFNbPpdYogv3I7zKAAAJAMBGGjaiYRBrk6SDVtrdiAAgBAChCEjaoZKRP8V07GloQAAJKBIGxUzU6Ewa8R6pUUq6JKB5VgTj0AQKghCBsl0twJBgNHAQAkAkHYKNaHF/TZ9AwGjgIASASCsFE54tcIMXAUACDkEISNyhVnNj2DxWUAACQCQdgw12x60WqERJhBAQAgAQjChrn2po8K9mx6BjMoAAAkAkHYsFzRZtMz2IACAEAiEIQNE282PYMtCQEAJAJB2LCanQjFqhHqFBSnJouDijGnHgAgpBCEDRN1Nj2TjBkUAAASgCBsGBvPKV7TKG8iWFQAAB21SURBVGHgKACANCAIGybe1hMuGDgKACAFCMKGNUmNEONlAABCD0HYALFn0zPVy42axHsHAADwDEHYADabPkG02fQMaoQAAFKAIGxAEwwZpZpVTDGnHgAgtBCEDWBTGkTagMnFVSNElRAAIIQQhA1gtbS2UeLWCKMUFK8mq5OKrKK+DwAAuIMgbEBWqUBEnWPEDUKqmUFxCXPqAQBCB0HYgKPFAhH1TRQ9CLvHcUT0WwmCEAAgZBCEdfFCdY2wV5zoQdgnniOiY8UIQgCAkEEQ1nW2QjDZqZ2OS9SI/l59EjiqqYACAEBIIAjrOlYiENH1CU3xXtcnVDeNIgkBAEIFQVgXa6hkjZZia6WlJC2VVdFFI6IQACA0EIR1sRoha7RsAqxSeAzjZQAAQgRBWNfRYqKmqhG63gjdhAAAoYIg/JMSG+WaBZ2CrjM0VRCyGmFx07wbAADUJdaq0kVFRatWrUpLSystLb3nnnvqnD19+vTu3btbtGihUCjGjRtHRLt3716/fn3Xrl3z8vJGjhw5dOhQkQrmHquZ9YrnZE2Ug2gaBQAIMbFqhA899NC0adPGjh2r0+mWLl1a+5TT6XzsscdmzZo1YcKErKysjIwMIsrLy+N5/ujRo0OGDAlVCtK1IaNNFYNEXWK4KAVdNAqltiZ7TwAAuEaUICwpKTlz5kxiYiIR3XDDDcuWLat99uDBgzExMQqFgoiuv/76//73v+z5t99++z//+c+oUaPEKJKXmnLIKCPnqEccJxAdL0WlEAAgBERpGs3OztZqtexYr9f//vvvtc+eOHFCp6ve+j06OvrkyZPseM+ePU6ns6ioaMaMGSwm67Pb7QUFBYcOHWIPU1NTExKCOeOviYeMMn3iuYOFwtFiYWirJn1fAAAgkYKwoqJCrVazY61WW1FRwfO8TCZr8GxZWRkRde/ePSEhITk5ecOGDU8//fTixYsbfOVz5859//33J06cYA/vvffe2bNnB6vYdp5OlqplHHVQVZp8XwjbYrGoVCq5XO7rD3bVy4kUmflVpvYOX3827JjNZo5D3ruDW+QRz/NWq1XAQhRueflFUqvVSqWyCcojZaIEocFgMJurN5w1m806nc6VgnXOmkym6OhoIurZsyerBd54440zZ85ctGhRg/8Lu3btGhMTs2DBAjGK/VuJUMU7OsVwSbE6P35cLpf7F4QDWgtEjpNGhV4v/qpuoSYIgl4v8k6PYQ63yCOe5+VyuathCRqEL5L3ROkjTEtLM5lM7NhoNHbo0KH22Y4dO1ZUVLBjk8nEziYnJ58+fZqI+BpiFMy9o03eQcj0SeA4oqxSwR6CDw0AEOlECcLWrVu70i4rK2vKlClEdPLkyRdeeIGIhgwZYjQaWdQdP36cnX3++ec7d+5MRL/++uvUqVP9qFcFrrqDsMmDMFpJHQyczUmnytHUAwDQ1MSaR/jRRx+tWLEiNTU1Ozv7mWeeISKtVssGtigUirfeeuvzzz+PiYkxGAwTJ04korFjx37++edEdPny5XfffVekUrnHhow25dwJlz7x3LkK4Wix0FP8vZ8AAKA2Lrw6nBcuXHjlyhWR+giTvrRftdDlaQq2cbyv/B4sQ0SvHuFfOuR8upfs7QEhqAo3JaPRyHqFoTG4RR7xPG+xWNBH6B6+SN7DEmvV/jALVy0Uryb/UjBA18cTER3F+jIAAE0OQVjtWAlRKDoIGdYee6QIQQgA0NQQhNWqh4yGooOQiFL0XIKaim2UV4ksBABoUgjCar+VCETUO0Q1QtdbH8U2FAAATQtBSEQkEO0tEIiof2LIgpBVRrExIQBAE0MQEhEdKRL+MAvtdFzP0NUIBydxRLTjD0yqBwBoUghCIqLNOQIRpSeHcoXHv7aTqWS0twD7MQEANCkEIRHRlss8EaWnhHIyu0FJQ1pxDp6256JSCADQdBCEVGilzCJBI6e/tAnx3UhPlhHRlhx0EwIANB0EIW25zPMCDW/DRYm13py3xrfniGhrDu9EFAIANBUEYXUNjNXGQqujgescw5XY6JerSEIAgCYS+t/+oWXnaecfPBGlJ0titeuxKRzV9FkCAEATiPQgzMgXyqqoRxyXGi2JIGQV083oJgQAaCqRHoRbcniqqYdJwS2tuFgVHS8RLhqRhQAATSHig/CyVDoIGaWMRrbD2FEAgKYjlQAIifNG4VS5EKemQS2lUiOkmt5KVlUFAACxRXQQbrokENGodjKFlG7DmGSZnKMf8gSTPdRFAQCIAFJKgCbHal0SGS/qkqihAS05m5N25aFSCAAgusgNwrIq+ilfkHP013aSuwlYYgYAoMlILgOazCfZvM1Jt7XhEjWhLko9bBTrhou8xRHqogAANHcRGoR2nt47wRPRk73koS5LA3rHcwNbckVW+uwMWkcBAMQVoUG4+jyfYxa6xHB/bSetDkKXJ3vJiOidLJ5H+ygAgJgiNAgXZfFE9ExvmURjkGhiqqyjgTtTLmzCcmsAAGKKxCD88YpwuEhoqaUZ10n348s5eryHjIgWHkcQAgCISLpJIJ6FvzmJ6LHuco0U+wevmd1FlqCmjHwBm1EAAIgn4oLwdLmwLVfQyGlOV6l/9ihFdSHfQaUQAEA0Ug+DoFt4nOcFmtlJlqQNdVG8MLenXCOn9Rf5cxWoFAIAiCKygrDQSl+c5TmiuT3D44MnaWlaR5lToHdPoFIIACCK8MiDYHntiNPioPQUrlusZIeL1vVkLxlH9Olp/qol1EUBAGiOIigI9xUIH5zklTL6V39pD5L5s55x3NgUmclOf9/vDHVZAACaoUgJQpuT5mQ4eYGe7SPrHR821UHmvcGyaCWtOc+vu4AGUgCAIIuUIHzpsPNkmdA1lnv2+nCqDjLt9dwbN8qJ6H/2OQutoS4NAEDzEhFBeLRYeOc4L+No2S1SnzvYmP/pJru1NVdopad+QQMpAEAwNf8gdPD0QIbTztO8nrLBSWHWKOoi42j5ULleSV+c5b+5hAZSAICgaf5B+NoR5+EioaOBe/WG8KwM1kiLrv4Ij/3Ml1eFujQAAM1FMw/C5af5147wMo6W3iKPUoS6NAF7vIdsUEvuD7Mw/UeHHdVCAIBgaM5B+O0lfs5ep0D070HyYa3DtVG0NjlHnw+Tt9DQ1hxh5h4ndmgCAAhcsw3C/VeF6T86HTy91E/2WPfm8zGvM3A7xyhiVbTqHP/Yzxg4AwAQqOaTELUdLxHStzsqHfRwN9nL/cK7a7C+3vHclr8qohT00e/8i4eQhQAAAWmGQVjF0+jtzlIbTekg+2Bwc0tBZnASt2q4XCGj147wb/2G3kIAAP81wyCUc5Sio4mpsi+GyaW7A33A/tZetuwWOUf0j1+dM/c4LY5QFwgAIDyF/0jKeuQc/fy3Zvi56ru3k0wtpwd+cn5+hs8qFdbfLm+vb77JDwAgjmZYI4wod3WQ7f+b4joDd7hI6P+NY1ceBpICAPgGQRj2esVzv45XjEnmiqw0cpvjob3OYluoywQAED4QhM1BnJo2jVS83E+u4Og/2XznNfYl2TxmGQIAeANB2EzIOHqpn+y3OxUj2nIlNnp4r/Ombx3bcxGGAAAeIAiblS4x3PejFV//RZ6i5w4VCaO+c/Td4Fh5jndghgUAQCMQhM3QpDTZyUmKt26St4nijhYLM350dvra8dZv/B9mVBABAOpCEDZPOgU901t2Yapi2VB5t1juolH4x6/OlK8ct291fHaGN9pDXT4AAMlAEDZnKhnN6izLulOx+a+KSWkylYx25Qn37XG2XGEf9Z3jvRP8uQrUEQEg0kXExPMIJ+MoPZlLT5aXVcnXXuC/OMPvLRC25wrbc52P76fOMdzw1tyQVtwtrTjMxweACIQgjCCxKprdRTa7i6zQSt/l8ltzhO9z+dPlwulyYUk2EVE7HTewJdcvkeubwPVN4JK0oS4xAID4EISRqIWG7rlOds915BTkBwuFvQVCRr6wL5/PNQtrLwhrL1Rf1kpLPeK4rrFc91iuayx3nYHa6bhmvHwrAEQmBGFEk3M0sCU3sCX3dC8SSP57mXCoSDhcJBwpFo4WC/kWyrcItZdtU8spLZrrEE0dorlkPddORyk6LllPrbScunnu8wEAzR+CEKpxRN1jue6x3D3XEREJRBeNQnYZnSwTssuE7HLhbLmQb6HsMiG7jJ3/kwQ1tYriWkdRKy2XqKGWWq6VlhLUlKDh4tWUoOYSNCRHbRIApEesIDxx4sSePXtat25ttVqnTZtW5+yuXbtyc3O1Wq3BYBg1ahQR5efnf/nll126dMnNzZ0zZ45MhuGsIcYRpUVzadE0OvlafJkddL5COG8ULpnosknIMVOuWbhsogKLUGyjYptwopTqZ6RLtJJilOp4jSNWRQYVGZScQUUxKopRcXoF6ZWkV1KsitPKSaugWBVpFaSVc9FKUuDrAACiESUIeZ6fO3fu9u3b5XL5u+++u2XLlvT0dNfZoqKiDz/8cN26dUQ0b9681NTUrl27PvLII5988klCQsLOnTsXLVr01FNPiVEwCJBOQb3iuV7xDdTsCix01SL8UUmFVqHQQgUW4aqViq1UYhOKbVRsFUpsZLST0c7lVrqS0tvJGzKOYlSkkpFOwanlFKUgrYI0ctLISSuvfoYjilUTEekVnFJGHEexKiIidpaIdApOJSMi0shJqyAiknNkUFW/BfspJk7tx70BgHAlShAeOnRIp9PJ5XIi6tWr15IlS2oH4ZYtWzp37syOO3XqtHr16rlz52ZnZyckJLDrn3rqKQRh2EnSUpKW6xVPRI02gBrtlFtisit1ZVVUZhMq7FRRRUY7lVYJJjuZHWSyU1mVYHGQxUllNrI4BauTKqrIKVBp9ZYa9bNTxKmQrnBlWO66HuqVpKxVVVXKSK/804+7oteFJbr7d6mqUqhUTnYco+IaqwwrZBStbORc9buTyouO2ziVDw3WserG/+82zvWXR4CUMtIrOCLiebJWcVVB/e0VrEJCOBLl/3x2drZOp2PH0dHRp0+fbuysXq/ft2/f2bNn1Wq165lTp0419soWi+XSpUs7d+5kD7t169a2bdvgfwAQR7SS2kUJ0dHsd6kPv1GdAlVUkY2nSodgcZDVSZUOsjmrk9LqJIuDeIHKq4iIjHbBIVx7aHNSpYOIyOQQ7DwREXsFInLw5Fpkh/0UUxO6JNQ6pmvPec+/kFYQYXFYj5REzXOFpDp/GPn/OoL6g5v5qR3Rr+CZKEFoNBpVquq/ezUaTXl5eZ2zsbGxrrNlZWVGo1GpVLqesdlsVqtVo9HUf+Xc3NwDBw4UFxezh1OmTLn77rvF+Ah+sFgsKpWK1YOhMWazmeP8GTOjJFIS6bmaoybBC1Rhv1Zaq5OstRLKaKfaq5nbBc7859/MlU6q+nOi1XlBRiAqr7r2pM1mc/1dWF4lNBaJToFzv1RepZOrcrq7oPqtfUmT8irOj2xnf6kEziFwJodYDQA2ngtKIQPX0J9f/uCIu1JhM5k8fAnUarXr12/EEiUIY2JizGYzOzaZTAaDofbZ2NjY2mdjYmLqXK9SqRpMQSLq1KnTlClTFixYIEaxAySXyxGEHgmCoNfrQ10KHxg8XxJkRqM9Orrh7z8wPM9bLBZXw1IzIxCVBSMILZWmNnHh9G8thEQJws6dOxuNRnZsNBo7depU+2ynTp2OHDlS+2xaWprFYmnsegCAyMEFabiWogorCXtLlObj/v372+12u91ORIcPH54+fToRbd++/fXXXyeicePGXbhQvXjJsWPHpkyZEhcX169fv6tXr9a+HgAAoAnIX3755aC/KMdxAwYM+O677y5evCiXy9k8QqvVKpPJunXrptVq27Zte/Dgwd9++61nz5633HILEQ0bNmzDhg1Xr149f/78E0880dg8wv3795tMppEjRwa9zIHLzMzkOC4mJibUBZEuq9W6a9euLl26hLogkrZr165WrVq5ugmhvqtXrx49ejQtLS3UBZG0zZs3d+3a1b8u+UjDCUI4VZ8XLlx45coVafYR3nfffbfccssDDzwQ6oJI19GjR2fOnHns2LFQF0TShgwZ8vrrrw8dOjTUBZGutWvXfvnllxs2bAh1QSStTZs2mZmZbdq0CXVBwgBG1gZTeP1VARCm8A8NggtBCAAAEQ1BCAAAES3M+ggfe+yxzZs3S3N+xcmTJ2NjY9Ei74bJZMrKyho4cGCoCyJpmZmZ1113nWvRCaivoKCgoKCgd+/eoS6IpGVkZAwYMMC1tkljUlJSli1b1jRFkqwwC8IzZ84cPnyYrUoqNQUFBXq9vrlO8g0KnudzcnLat28f6oJIWk5OTuvWrRUKLHzZKKvVWlpa2rp161AXRNIuXLjgzcBag8Fw0003NUF5pCzMghAAACC40EcIAAARDUEIAAARDUEIAAARDUEIAAARDUEIAOHKZrNVVVWFuhQQ9jBE27PDhw9nZmYuW7bswIED9c+uX7++uLg4MTExJyfn8ccfJ6JLly4tX758wIABhw8ffvjhhxMSEpxO57/+9a/rr78+Pz+/U6dOw4cPb/IPIS6j0bh9+/YtW7bceuut9913X52zJpPpzTffHDRoUHZ29qhRo7p3787z/KeffqpQKA4ePJiamvrMM88Q0f/93/8dOHCgdevWVqt18eLFKSkpIfgkYvrpp58OHjy4d+/eBhfJXLJkicFgkMlkNpvt3nvvJaJXXnnlhx9+aNu2rcViWbBgQceOHV138tSpUyNHjuzRo0eTfwhxXb169Ycffvjiiy+effbZIUOG1Dmbl5e3ZMmSgQMHHj16dNasWUlJSbt27Xr00UeTk5PZGuWDBg169dVXp02bVlpaGh8fLwjCf/7zn+jo6FB8FBFt3bp1//79ZWVl7733Xp1TFotl27ZtO3bs6Nq169y5c9mTW7ZsuXz5cuvWrS9cuPDEE09wHJeXl/fxxx8PHDjw2LFj999/f6tWrZr8Q0iMAJ788ccfhYWFycnJ9U+Vl5ePGjWKHS9evHj9+vWCINx55515eXmCIFy+fHnGjBmCIKxYseL9999nl40aNcpsNjdR0ZtKZWVlXl7e008/vWzZsvpnX3zxxe+//14QBLvdfttttwmCsGrVql27dgmCwPN8165dt2/fLgjCokWLPv/889WrV5tMpqYtfhO5dOnSwYMHhw8fXv9Udnb2/fffz44ff/zxI0eOCILw7rvvrlixYtWqVRUVFezUyy+//N133wmC4HA42J1sZsrLywsLC++44449e/bUPzt9+vTz588LgnD16tVJkyYJgrBkyZLvv//+wIEDmZmZb7zxxvHjxwVBmD9//vLlyzdu3FhVVdXE5W8aFy5cWLNmzYMPPlj/lNVqzc3NffXVVxcuXMieqaysdH1VPvnkkxUrVgiCcPfdd589e1YQhMLCwjvvvLOpCi5daBr1rE2bNhpNwzuG//DDD64/plJTUzds2GCz2fbu3cum+iYnJ2/dutXpdH777bedO3dmlxkMhj179jRNyZuMVqt1M7vZ9fEVCkVJScn58+crKipWrlxJRBzHde/enW3UrNfr77nnnilTpjTXRQlSUlIamya/adOmjh07ui7buHEjEWm12hkzZkydOtVVp3HdSblcXl5efvbs2SYpeNMxGAyJiYkNnnI6ndu3b2czxFu0aLFnzx6bzXbLLbeMGDHipptuat26dfv27Xv27ElESUlJ991337hx45RKZZOWvqmkpqY2trmSWq1u27Zt7WcyMjJcK5CkpqauX7+e5/mtW7ey71tiYmJGRobVahW7zBKHIAzIhQsX9Ho9O9br9RcvXiwoKKi9mSLP8yUlJRcuXHD9ctfr9ZcuXQpBWUOnzse/ePHinDlzli5dSkQOh+PQoUNsT8ry8vKvv/5648aN//rXvyKt46f+LSIis9n89ddff/vtt6+99hr7VVX7Mp1Oxy6LECUlJU6n0/VQLpcXFBR069aNPVy+fPnUqVPZcU5Ozvr169evX//OO+8IEb9gyMWLF+v8jiotLXU4HK4LFApFfn5+iEonFQjCgFgsFlfsKZVKs9lssVjkcrnrApVKZTKZaj/JLgtBWUPHzcd/8803Z82aNXjwYCKaMGHC5MmT//a3v2k0mrfffjs0ZQ2RBm/RuHHjJk2aNH78+MTExPnz59e/zGQyharATc9isdSuT9f++Hv27ElMTHRVkmbOnDlx4sSJEyeePXt2zZo1ISirlHj8HRVpX6QGIQgDEh8f7/oOGY3GuLi4+Ph4o9HouqCiooI9WfuySFtPuf5dYsd79uzRarUvvvgiEfE8X1ZWxp7v0KHD1q1bQ1LUUGnwFpWUlLBf7q4b0tidjAR1/mUZjcb4+Hh2/NFHH91www3s2GKxWCwWdpyWlhZpX6T6PP6OirQvUoMQhAHp3bt3RUUFO66oqOjdu3dCQoLBYOB5noiqqqqSkpJiY2N79+5dXl7OLjMajZG2an7tu1RZWcnGOmZlZRUWFj755JNE9N133505c4YNLGLXRNrfCvW/SJcvX548eTJrwqqsrIyJiSGiPn36uL5IZrO5+Y0adUOv17dp08ZmsxERz/M6nS4pKYmd2rlzpysUf/jhh3/84x/sOAK/SPXV/2pFRUWlpqZWVlYSkSAIGo0Gy5cjCL2Sk5NjNBpLS0vZwx07dkyYMIGIBg0aVFlZyf4C3bt373333SeTyWbNmpWRkUFEP/zww5w5c4jogQce2Lt3LxGZTCaHw+H667U5qaqqKigoyMvLc3U/jBkzht2HBx988McffySiS5cu9e3bNy4u7tKlS4888siOHTseeuihu+66y+FwdOjQ4ZlnnuE4ThCEjRs3Pv3006H8MKLJyckpKipyNQ4vXbr0iSeeIKLx48f//vvv7O+Ao0ePTpo0qV27ds8//zxrDPzmm2/YDJMHH3xw9+7dRHT58uXevXs3Nq4krFkslsLCwpycHHY3nE5n3759L1y4QERz5sxh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      ]
     },
     "metadata": {},
     "execution_count": 5
    }
   ],
   "cell_type": "code",
   "source": [
    "varied = (ω => range(0.99, 1.1, 100))\n",
    "fixed = (α => 0.0, β => 1.0, ω0 => 1.0, γ => 0.005, F => 0.0025)\n",
    "\n",
    "result = get_steady_states(harmonic_eq, varied, fixed; threading=true)\n",
    "plot(result; y=\"u1^2+v1^2\")"
   ],
   "metadata": {},
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "## 2nd order Krylov expansion"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "The quadratic nonlinearity $\\beta$ together with the drive at 2ω gives the effective parametric drive $\\lambda_\\mathrm{eff}=\\frac{2F_1\\beta}{3m\\omega^2}$. But the cubic nonlinearity $\\alpha$ is still needed to get the period doubling bifurcation through $\\lambda_\\mathrm{eff}$."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "A set of 2 harmonic equations\nVariables: u1(T), v1(T)\nParameters: ω, ω0, F, β, α, γ\n\nHarmonic ansatz: \nxˍt(t) = \nx(t) = u1(T)*cos(ωt) + v1(T)*sin(ωt)\n\nHarmonic equations:\n\n(-(1//6)*F*v1(T)*β + (5//12)*(u1(T)^2)*v1(T)*(β^2) + (5//12)*(v1(T)^3)*(β^2) + (1//8)*v1(T)*(γ^2)*(ω^2) + (1//8)*v1(T)*(ω^4) - (1//4)*v1(T)*(ω^2)*(ω0^2) + (1//8)*v1(T)*(ω0^4) - (3//8)*(u1(T)^2)*v1(T)*α*(ω^2) + (3//8)*(u1(T)^2)*v1(T)*α*(ω0^2) - (3//8)*(v1(T)^3)*α*(ω^2) + (3//8)*(v1(T)^3)*α*(ω0^2) + (51//256)*(u1(T)^4)*v1(T)*(α^2) + (51//128)*(u1(T)^2)*(v1(T)^3)*(α^2) + (51//256)*(v1(T)^5)*(α^2)) / (ω^3) + (-(1//2)*u1(T)*γ*ω + (1//2)*v1(T)*(ω^2) - (1//2)*v1(T)*(ω0^2) - (3//8)*(u1(T)^2)*v1(T)*α - (3//8)*(v1(T)^3)*α) / ω ~ Differential(T)(u1(T))\n\n(-(1//6)*F*u1(T)*β - (5//12)*(u1(T)^3)*(β^2) - (5//12)*u1(T)*(v1(T)^2)*(β^2) - (1//8)*u1(T)*(γ^2)*(ω^2) - (1//8)*u1(T)*(ω^4) + (1//4)*u1(T)*(ω^2)*(ω0^2) - (1//8)*u1(T)*(ω0^4) + (3//8)*(u1(T)^3)*α*(ω^2) - (3//8)*(u1(T)^3)*α*(ω0^2) + (3//8)*u1(T)*(v1(T)^2)*α*(ω^2) - (3//8)*u1(T)*(v1(T)^2)*α*(ω0^2) - (51//256)*(u1(T)^5)*(α^2) - (51//128)*(u1(T)^3)*(v1(T)^2)*(α^2) - (51//256)*u1(T)*(v1(T)^4)*(α^2)) / (ω^3) + (-(1//2)*u1(T)*(ω^2) + (1//2)*u1(T)*(ω0^2) - (1//2)*v1(T)*γ*ω + (3//8)*(u1(T)^3)*α + (3//8)*u1(T)*(v1(T)^2)*α) / ω ~ Differential(T)(v1(T))\n"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "cell_type": "code",
   "source": [
    "@variables β α ω ω0 F γ t x(t)\n",
    "diff_eq = DifferentialEquation(\n",
    "    d(x, t, 2) + ω0^2 * x + β * x^2 + α * x^3 + γ * d(x, t) ~ F * cos(2ω * t), x\n",
    ")\n",
    "\n",
    "add_harmonic!(diff_eq, x, ω)\n",
    "harmonic_eq2 = get_krylov_equations(diff_eq; order=2)"
   ],
   "metadata": {},
   "execution_count": 6
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=5}",
      "image/png": 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",
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      ]
     },
     "metadata": {},
     "execution_count": 7
    }
   ],
   "cell_type": "code",
   "source": [
    "varied = (ω => range(0.4, 1.1, 500))\n",
    "fixed = (α => 1.0, β => 2.0, ω0 => 1.0, γ => 0.001, F => 0.005)\n",
    "\n",
    "result = get_steady_states(harmonic_eq2, varied, fixed; threading=true)\n",
    "plot(result; y=\"v1\")"
   ],
   "metadata": {},
   "execution_count": 7
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\rSolving via total_degree homotopy ...   1%|█                                                 |  ETA: 0:01:12\u001b[K\rSolving via total_degree homotopy ...   3%|██                                                |  ETA: 0:01:09\u001b[K\rSolving via total_degree homotopy ...   4%|███                                               |  ETA: 0:01:04\u001b[K\rSolving via total_degree homotopy ...   6%|████                                              |  ETA: 0:01:02\u001b[K\rSolving via total_degree homotopy ...   8%|████                                              |  ETA: 0:01:00\u001b[K\rSolving via total_degree homotopy ...  10%|█████                                             |  ETA: 0:00:58\u001b[K\rSolving via total_degree homotopy ...  11%|██████                                            |  ETA: 0:00:57\u001b[K\rSolving via total_degree homotopy ...  13%|███████                                           |  ETA: 0:00:55\u001b[K\rSolving via total_degree homotopy ...  15%|████████                                          |  ETA: 0:00:53\u001b[K\rSolving via total_degree homotopy ...  16%|█████████                                         |  ETA: 0:00:52\u001b[K\rSolving via total_degree homotopy ...  18%|██████████                                        |  ETA: 0:00:51\u001b[K\rSolving via total_degree homotopy ...  20%|██████████                                        |  ETA: 0:00:50\u001b[K\rSolving via total_degree homotopy ...  22%|███████████                                       |  ETA: 0:00:48\u001b[K\rSolving via total_degree homotopy ...  23%|████████████                                      |  ETA: 0:00:47\u001b[K\rSolving via total_degree homotopy ...  25%|█████████████                                     |  ETA: 0:00:46\u001b[K\rSolving via total_degree homotopy ...  27%|██████████████                                    |  ETA: 0:00:44\u001b[K\rSolving via total_degree homotopy ...  29%|███████████████                                   |  ETA: 0:00:43\u001b[K\rSolving via total_degree homotopy ...  30%|████████████████                                  |  ETA: 0:00:42\u001b[K\rSolving via total_degree homotopy ...  32%|█████████████████                                 |  ETA: 0:00:41\u001b[K\rSolving via total_degree homotopy ...  34%|██████████████████                                |  ETA: 0:00:40\u001b[K\rSolving via total_degree homotopy ...  36%|██████████████████                                |  ETA: 0:00:38\u001b[K\rSolving via total_degree homotopy ...  38%|███████████████████                               |  ETA: 0:00:37\u001b[K\rSolving via total_degree homotopy ...  39%|████████████████████                              |  ETA: 0:00:36\u001b[K\rSolving via total_degree homotopy ...  41%|█████████████████████                             |  ETA: 0:00:35\u001b[K\rSolving via total_degree homotopy ...  43%|██████████████████████                            |  ETA: 0:00:34\u001b[K\rSolving via total_degree homotopy ...  45%|███████████████████████                           |  ETA: 0:00:33\u001b[K\rSolving via total_degree homotopy ...  47%|████████████████████████                          |  ETA: 0:00:32\u001b[K\rSolving via total_degree homotopy ...  49%|█████████████████████████                         |  ETA: 0:00:31\u001b[K\rSolving via total_degree homotopy ...  50%|██████████████████████████                        |  ETA: 0:00:29\u001b[K\rSolving via total_degree homotopy ...  52%|███████████████████████████                       |  ETA: 0:00:28\u001b[K\rSolving via total_degree homotopy ...  54%|████████████████████████████                      |  ETA: 0:00:27\u001b[K\rSolving via total_degree homotopy ...  56%|████████████████████████████                      |  ETA: 0:00:26\u001b[K\rSolving via total_degree homotopy ...  58%|█████████████████████████████                     |  ETA: 0:00:25\u001b[K\rSolving via total_degree homotopy ...  60%|██████████████████████████████                    |  ETA: 0:00:24\u001b[K\rSolving via total_degree homotopy ...  61%|███████████████████████████████                   |  ETA: 0:00:23\u001b[K\rSolving via total_degree homotopy ...  63%|████████████████████████████████                  |  ETA: 0:00:22\u001b[K\rSolving via total_degree homotopy ...  65%|█████████████████████████████████                 |  ETA: 0:00:21\u001b[K\rSolving via total_degree homotopy ...  67%|██████████████████████████████████                |  ETA: 0:00:19\u001b[K\rSolving via total_degree homotopy ...  69%|███████████████████████████████████               |  ETA: 0:00:18\u001b[K\rSolving via total_degree homotopy ...  71%|████████████████████████████████████              |  ETA: 0:00:17\u001b[K\rSolving via total_degree homotopy ...  72%|█████████████████████████████████████             |  ETA: 0:00:16\u001b[K\rSolving via total_degree homotopy ...  74%|██████████████████████████████████████            |  ETA: 0:00:15\u001b[K\rSolving via total_degree homotopy ...  76%|███████████████████████████████████████           |  ETA: 0:00:14\u001b[K\rSolving via total_degree homotopy ...  78%|███████████████████████████████████████           |  ETA: 0:00:13\u001b[K\rSolving via total_degree homotopy ...  80%|████████████████████████████████████████          |  ETA: 0:00:12\u001b[K\rSolving via total_degree homotopy ...  82%|█████████████████████████████████████████         |  ETA: 0:00:11\u001b[K\rSolving via total_degree homotopy ...  83%|██████████████████████████████████████████        |  ETA: 0:00:10\u001b[K\rSolving via total_degree homotopy ...  85%|███████████████████████████████████████████       |  ETA: 0:00:09\u001b[K\rSolving via total_degree homotopy ...  87%|████████████████████████████████████████████      |  ETA: 0:00:08\u001b[K\rSolving via total_degree homotopy ...  89%|█████████████████████████████████████████████     |  ETA: 0:00:06\u001b[K\rSolving via total_degree homotopy ...  91%|██████████████████████████████████████████████    |  ETA: 0:00:05\u001b[K\rSolving via total_degree homotopy ...  93%|███████████████████████████████████████████████   |  ETA: 0:00:04\u001b[K\rSolving via total_degree homotopy ...  94%|████████████████████████████████████████████████  |  ETA: 0:00:03\u001b[K\rSolving via total_degree homotopy ...  96%|█████████████████████████████████████████████████ |  ETA: 0:00:02\u001b[K\rSolving via total_degree homotopy ...  98%|██████████████████████████████████████████████████|  ETA: 0:00:01\u001b[K\rSolving via total_degree homotopy ... 100%|██████████████████████████████████████████████████| Time: 0:00:58\u001b[K\n"
     ]
    },
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=1}",
      "image/png": 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4pRFNTUNhYeGcOXMMC0NDQ9esWaN/y7LssmXL9u7d6+LiYtisX79+ISEh1tbWYWFhQUFBv//+u1arZVmWq5VIJBqNRuihiJ1RAuH169etra25bQcHh4sXLxrWXrx4UZ/MOTo6Xrx4sba29vfff7exsSEiiURSWVlZXl4+d+5crs2PP/44a9YsC4s/k9fTp08rFIphw4Z5e3sbo/MAAB2Ulb21k5NTbGysYWFgYKDh261bt65cubLpjNXJkycHDhzo7e3dpUsXlUp1+/ZtNzc3/TpSpVLZtWtXo3a+HRklEMrl8i5dunDbMplMLpczDKOPZI1qKysr5XI5NxHIkUqllZWV3bp1I6LKysrbt28/9dRTXJVKpRowYICzs3NMTMzWrVt79OjRbAfKysoCyMMYhwYA8NdpNBpbW9vW2wi4swwrsXB0dGwUCA0lJiZOmDAhJCRELpenp6dHR0fre/L111+/8cYb3t7eDQ0NGo3Gx8cnPDw8PT2d2/HBgwdNY2enYZQ5QltbW7VazW2r1Wpra2t9FGxaa2tra2dnpy/RF3Lb8fHxw4YN01e98sorrq6uFhYWYWFhW7ZsaakDXBAFABCnh0ZB+t/FMrxerV8+kZiYuHr16uXLlz/22GNhYWHBwcFEFBERkZSURETz5s2TyWRE9MUXX6xdu9bJyWnq1Kn5+fl1dXVqtTo3N3fGjBltdPSiY5SMsHv37oYJdaMxzO7duysUCn2tl5eXq6srwzA6nc7S0pKI6urq9JFs375906dP57avXLmyefPmnTt3EpGtrW1paWlLHZBIcHsFAID/Y8CAAdzfT46/vz8RHTx4kFuxMWXKlLS0tB9++GHo0KGjRo0iIjs7ux07dpw9e1alUsXHx+tH8jofowTCXr16OTk5abVaKyurwsLC6OhoIqqoqEhNTZ0+ffr48eM/+ugjrmVBQUF0dLSlpeWUKVOKi4v9/PwqKiqGDh3K/TDRarWZmZmGM7r6RTf5+fmRkZHG6DwAgBgIuMVa6+0DAgKaFnp5eem3R44cOXLkSMNaJyenqKgoXn3oiIx1+cSGDRs2b958+fLlffv2vf3220SUn5+/Z88eIpLJZPPmzfvuu+9SU1Nv3rz50ksvce23b9+ekZHx8ccf68c86+vrLS0t9StrhgwZYmVl9fPPP8fHxzs5Ob344otG6jwAQLtjiPfQKB7DJIxEvzq2zbEsW15e3q1bt2YHKnU6nX5FjN79+/ddXFysrP6bp9bW1uovZOEolUorKyvDxTVNjQoaK80308Uy+Z+E//UPuT03/q9/CAC0xMIz76FtPsxJ+LUyg9fHKvLl5ZtuZmZmCu2XmTLiLdYkEomHR4vRyNLSsumSFnd390YljaIgETk4OLRJ9wAAAAj3GgUAECchT6g3Ulc6OwRCAAAxYghPqDcRBEL4E+YFAUQFD+Y1Gfx8AAAAs4aMEABAjIQ8hgmXTwiCQAgAIEYCrgtEIBQGgRAAQIxY/oHNaJeFd3KYIwQAALOGjBAAQIzYhz1NotldjNSZzg2BEABAjFiStO1Nt6ElCIQAAGLE8L+zDK4jFAZzhAAAYNaQEQIAiBFLuHzCRBAIAQDECItlTAaBEABAjAQ8fQLXEQqDOUIAADBryAgBAMQIc4Qmg0AIACBGLBHfkU6MjAqDQAgAIEZCnj5BEqSEAmCOEAAAzBoyQgAAMWJZ/pdDYI5QEARCAAAxEvZgXksj9aZTQyDsbAKX/6rfzv8kvB17AgB/BUsCLqg3Ul86OcwRAgCAWUNGCAAgRixLDM8MDxmhMAiEAABiJGCxDO41KgwCIQCAGAmZI8TzCAXBHCEAAJg1ZIQAAGIk7PIJI3Wmc0NGCAAgRqygV+u0Wm1OTk5lZWWztWq1+saNGwqFQl+ib1lZWcl23qU4CIQAAGLELZbh9Wr9zjJlZWUJCQmVlZVvv/32qlWrGtVev379xx9/rKysXLBgwY4dO7jCESNGBAYGDhgw4JNPPpF03vuYYmgUAMAsbN26NTo6evTo0WFhYT4+PjExMcOHD9fXbtmy5fXXX+/du3fv3r39/Pxmzpzp4uISFxcXERHh5+fn6enZjj03NmSEAADixC8d/DMpbJmXl1dubi4RWVlZubu7FxYWGtY6OztzJe7u7kR07949InJ0dBwyZIiLi4sRj1IEkBECAIgRy/K+QL719nFxcdzG3bt379+/P378eMPaDz/8kNv45ZdfgoOD+/TpQ0RXr15NSUlRqVSZmZnvvPMOv950HAiEAABi9NAMrymdSlNQUDBnzhzDwtDQ0DVr1hh8LLts2bK9e/c2m+fV1tauX7/+wIEDFhYWRLRhwwaZTEZEO3fuPHHixMSJE4UcieghEAIAdBIWdjbOzs6xsbGGhYGBgYZvt2zZsnLlyrCwsKa7MwyzYcOGr7/+2t/fn4hu3bpVXFz82GOPEZGHh0daWhoCIQAAmBL/O8tILBwdHRsFQkOJiYmRkZEhISFyuTw9PT06Olqj0dja2nK1O3fuXLp0qbu7+4ULFzw9PY8cOcKyLBcIHzx4MG7cuL9wLKKGQAgAIEZtPkeYmJi4evVqLy+vhoaG4uLi5ORkIoqIiFi9evX06dM//PDDPXv2/Oc//1Gr1WVlZTk5ObNnz05NTSWimzdv1tXVPfXUU8IPRtwQCAEAzMKAAQN27typf8uNfx46dMjNzY2InnjiicjISK7KxsbGwsKie/fuI0eO3LNnj0QiSUpKsra2bo9emwICIQCAGAl4+kTrF9QHBAQ0LdRfINivX7+mtb6+vr6+vvz60AEhEAIAiFTbDo1CSxAIAQBE6WG3TGt+F+APd5YBAACzhowQAECMBFxQjwfzCoNACAAgRo/yWKWmu4AACIQAAGKFOUKTwBwhAACYNWSEAACi1NZ3loGWIBACAIgSJglNBYEQAECMWP433UYgFAZzhAAAYNaQEQIAiBKGRk0FgRAAQJQE3GINF9QLgkAIACBGLG66bSqYIwQAALOGjBAAQJRY3FnGRBAIAQBECYtlTAWBEABArBAITQJzhAAAYNaQEQIAiBKeUG8qCIQAAKIkYI4QBEEgBAAQJSyWMRXMEQIAgFlDRggAIE6YIzQRZIQAAGDWkBECAIgS5ghNBRkhAACYNWSEAACihIzQVBAIAQDESEIk4bn4BUtlhEEgBAAQJWSEpoI5QgAAMGvNZIR37959++23e/To4evrO2HChICAANN3CwDA3CEjNJVmAmFJSUl+fv67777r6upqbW1t+j4BAABR2wdCrVZ7+/Ztd3f3rl27Nlubk5Pj6+vr5OSkL7xz5w4R+fv78+xKR9L80Oj8+fN9fX2lUqmNjY3gj87Lyzt//rxWq222NiMj47fffjMsKS4uPn36dE1NDfdWo9EUFhYSEcMwv//+u77ZlStXLl26JLhXAAAdA/f0Cb6vlpWVlSUkJFRWVr799turVq1qWvvaa69JpdL9+/cfPXqUK1yxYkVJSUlpaen7779vrMMUgeYDof7HwoEDB06ePFlXV8f3cz/88MM//vijb9++b7zxhlKpbFS7bNkyKysrd3f3119/nWEYItq3b9/PP/88fPjwDz74gPsBkp+f7+fn5+XlFRoaWlJSwu24ZMkSe3t7FxeXN998k2UxCgAA8Ki2bt06YMCA0aNHf/rppzt27GiUimzcuHHWrFk9e/Z88cUX33nnHZ1Ol5aWVldXN2rUqPDw8KqqqrNnz7ZXz42t+UBoYfFn+bRp027fvu3p6blu3brLly8/4odWVVUdPXo0Kiqqa9euY8eO3bx5s2Ht5cuXa2trQ0ND/f39XV1dDxw4QEQbNmx46aWXpFLp888/r/+pcuzYsbS0tMzMzIiICCK6cOECEfXt2zcwMNDe3v7w4cOCDhkAoAOQsLxfrQ+Nenl55eXlERGXh3BDbnopKSndu3f/85+WSK5du5acnOzj48OVeHp6pqSkGOU4RaD5QKjT6bgNS0vLhQsXzpo1a926dUOHDn3EDz1//rw+p3R3d//ll18Ma3/55RdPT0/D2tu3b6tUKi76GrZ3cHCwtrZWq9Ut7fiI/QEA6JBYnq9WxcXFzZs3j4ju3Llz//798ePHG9YWFxfLZDJuWyaTlZSUlJSUSKVSw5K2P0BxaP46wo8++kihUDz22GPczwH9jwJOdXW14VRqU6WlpfrT5+DgUFpa2qi2W7duhrVlZWWGp/v+/fs6nU4ikRw7dmzmzJk//PCDn5/fU089VVpa2qtXr5Y+1pBcLpeSRys9BABoRw0NDQ9fish/1Shbpy4oKJgzZ45hYWho6Jo1a/7bhmWXL1++b98+FxcXw2ZarVY/3ySRSOrr6xuVaDQafr3pOJoPhNnZ2S+++KJWq+3Vq9djjz1WXV1dUlLi7e3N1X788cf//Oc/W/lQhmH0OSXLso3WyxjWMgyj1WobtefeBgcHr1u3zsLCon///j4+Po8//njTHVvqgFQqpQcPP3gAgHZhZWWUm5lIbGydnZ1jY2MNCwMDAw3fbtmyZeXKlWFhYY32dXNzUyqVXl5eRKRUKrt27cqVcLVciTH6LAbN/8f48ssvIyMjz507d+bMmdOnT1+5cmXv3r1BQUHjxo0bN25cTk5O6x/q7u6uP30KhcLd3b2lWqVS6ebm1qi9k5OTjY3Nnj17Bg8eHBQUZG1tbWFhwS35bbRjSx2wtbV9hGMHAGgfEskj3A2Nm/bj+bGOjo6NAqGhxMTEyMjIkJAQuVyenp4eHR2tVqvt7OyIaOTIkQ8e/JlA1NTUDBkyRC6X//rrr1yJXC4PDw/n15uOo5k5wv79+48cOdLBwWHq1Kn/+te/0tPT5XL5kSNHZsyYkZWV9eKLL+pX1rZk1KhR1dXV3HZlZeWoUaOIqKGhgTvLY8aMkcvlXG1FRcXo0aODgoL0oauysnL06NFEdPToUe5SioaGBpVK5e/v33THv378AADixXeOsNXAeeDAgdWrVy9fvnzcuHEjRowIDg4mojFjxiQlJRHR0qVLExMTiSgjI2Py5MkODg7R0dH5+fkqlaquri4vLy8mJsYkx9wOmskIHR0dHR0dDUu4MxIdHU1ESqWSm25thYeHx6BBg7Kysvr27XvkyJHVq1cTUXx8/IkTJxITEyMiIhISErh5waysrOXLl1taWr788stJSUnTp0//4Ycf/vGPfxDR/Pnz6+rqdDrdJ5988t5777m4uEyYMOGbb76pqKiwsbHJy8vjmgEAwKMYOHDgzp079W+5a+QPHTrEja6NGDHC2dk5JSVFp9Nt3LiRiOzs7Hbs2HH+/HmVSpWQkNClS5d26rjRSQRcjffOO++sXbu29TYsy168eLGiomLYsGEeHh5ExDCMWq3mTmV9fX16erpCoRg3bpx+nVJWVlZRUVFQUJB+RcyNGzcyMzMHDBjQr18/rkSj0aSnp9fU1IwbN06/vqapUUFjpflYLEP5n/AYyrg9N954PQEAQxaeeQ9ts+jgoeRbt3h9bP29e64pyZmZmUL7ZaaEBEKGYfQXGooTAiEHgRBAnB4lEC5OEhIIXY4jEPImZOWSyKMgAEAngdtnmQRCGgAAmDU8mBcAQJTwGCZTQSAEABAjCdEjXGzYeBcQAIEQAECUkBGaCuYIAQDArCEjBAAQK2SEJoFAaNZw7SCAeAm41ygCoSAIhAAAoiRgjhAEwRwhAACYNWSEAABihTlCk0AgBAAQIwn/OUIEQmEQCAEARIklYnleIs+3PRAR5ggBAMDMISMEABAjCf/LIXD5hDAIhAAAooRbrJkKAiEAgCjhOkJTwRwhAACYNWSEAACihFusmQoCIQCAWGGO0CQQCAEARAmLZUwFc4QAAGDWkBECAIiRgFusYY5QGARCAACxwtCoSWBoFAAAzBoCIQAAmDUMjQIAiJGQOULj9KTTQyAEABAlXD5hKgiEnVng8l/12/mfhLdjTwBAAKwaNQ3MEQIAgFlDRggAIEoYGjUVZIQAAKLECno9THl5ebPlOTk5jUpqaqS0AuoAAB3iSURBVGo0Gg0RMQxTWVn5l49HvBAIAQDESPK/C0cf/dW65OTkzZs3Dx06tGkVwzBDhgyRSqWurq6urq49e/ZUKBRJSUnu7u6hoaERERFlZWVGOUhxwNAoAIBZiIqKioyMfP/995tW3blzZ+fOnRMnTiSi27dvFxYWOjo6siybmpqq0+lCQ0MtLS1N3l/TQSAEABAlE84Rurq6Tps2zdbWVqvVpqWlLV26lCvv3bu3Vqvt3FGQMDQKACBOfMdFBVyAr+fs7Gxra0tECQkJc+fO/bMDEsmuXbsuXbq0fPny7OzstjouEUJGCAAgVjwDG6NWFxQUzJkzx7AwJCRk7dq1j7J7bW1tamrq4sWLubcxMTFSqZSIHBwcFi5cmJqayq83HQcCIQBAJyGxsXF2do6NjTUsDAwMfMTd9+/f7+Pjo3+bmJjIxUJPT8+LFy/qdLrOOkaKQAgAIEr85wglZOHo6NgoELZOrVbb2dlx22fPnjWMmp9//vn48eOlUqlcLvf19e2sUZAwRwgAIE5tPkdYUFBw5MgRhUJx8uTJkpISIjpy5Eh4+H9vvlhSUiKTyfRvlyxZYmlpyTBMfHz8Rx99ZLQDbX/ICAEAzEX37t0Np/qioqIGDx6sf/vaa68FBQXp3z799NMpKSnl5eWLFy/u27evSTtqWgiEAABi1aa3TPPz8/Pz8zMssbS09PLy0r+NjIxstMvkyZPbsgdihUAIACBKAp5HiHuNCoJACAAgSrjptqlgsQwAAJg1ZIQAAGKFjNAkEAgBAMRIwpKE5RfZ+LYHDgIhAIAoYY7QVDBHCAAAZg0ZIQCAGEn4Xw4hMU5POj0EQgAAUcLQqKkgEAIAiJKA5wsiEAqCOUIAADBryAgBAMQKGaFJIBACAIgS5ghNBYEQAICHKO+Bf/1DjjMPb/PQ5ws2s4uw3pg9zBECAIBZQ0YIACBKGBo1FQRCAAAxEnJBPQKhIAiEAACihIzQVDBHCAAAZg0ZIQCAKAlYNYqMUBAEQgDotNrkUof2hKFRk0AgBAAQIwnL8n4wLyKhIJgjBAAAs4aMEABAlLBq1FQQCAEAxEjAdYQIhMIgEAIAiBIyQlPBHCEAAJg1ZIQAIAod/lKHNofrCE0FgRAAQKwwNGoSCIQAAGIk7HmECIUCYI4QAADMGjJCAABRYlnieWcZ3u2BiIwXCLOysn7++efQ0NDs7Ozly5fb2NgY1iYnJ+fn53t5eRUVFb3yyitEVFZW9vnnn4eFhWVmZi5YsMDNzU2tVu/cudPKyur8+fPR0dFz5swhohdeeKGqqsrFxUWr1f773/92dHQ0Uv8BANqXsOcRPnSP8vLybt26NS2vqKhwc3MjopqaGktLS3t7eyJSqVT5+fmBgYFdunTh15UOxVhDo8uWLXvttdeeeOKJ8PDw9evXG1ap1eqNGzcuXrx4xowZ1tbWu3fvJqIVK1Y899xzU6dOffHFF5csWUJE27Zti4yMnD9//pYtWxYvXnzr1i0iCgwMjIqKevzxx7dv344oCACdGSvo1bLk5OTNmzcPHTq02dqFCxd6enqGhITExcVZWFgQ0dWrV9evX+/i4vLpp59mZ2cb4xBFwigZYVFR0f37921tbYkoICBgyZIl69at09eeO3eua9eu3HZAQMCXX34ZGxt7+PDhb775hog8PDxOnTql0WiKi4u///77devWOTg4+Pj4XLt2LSgoyNvbe/78+cboMwDwgqsdOpyoqKjIyMj333+/2drIyMg1a9a4uLj4+/tzJStXrvz+++/d3NyWLl06ffr0X375xXR9NS2jBMLff/9dKpVy2w4ODn/88UfrtXK5vL6+Xt/A0tKytLR006ZN3FuFQnHnzp1hw4YRUXFxcWJiIhEVFRVxiWOz6urqpG16RAAAbYhhGC7rao1pryO0tbUdNGhQXV0d97a+vj4tLY0bLJXJZFevXq2trdX/6e5kjDI0qlKprKz+DLHW1tYqlYphGH1tXV2dpaWlvrampsawvb5Q/3bFihWbNm3ifqTMnTs3JiYmJiYmOzt73759LXVAo9G06QEBALQlwz+JrWm7cdGHunPnTlJSUmpq6uLFi9VqdUVFhbW1tb7Wzs6uvLz8L/0DImaUjNDV1VWpVHLbSqXS0dHR8LePi4uLPs4plUpnZ2fD9lyhi4sLt/3TTz+FhYW98MIL9H/DW69evQ4ePDh79uxmO+Ds7EyVbXlEAABtyPCnf0skLPF9HqGuvq6goIBbWqgXEhKydu3ah+771ltvcQnfmTNnPv/889mzZzeK1objdp2MUQJh79699UFLqVSGhoYa1oaGhu7du5fbVigUoaGhMpmse/fuarXazs6OZVk7OztPT08iSk1Nlclks2bNUqlUly5dqq2t/fTTT5OTk4morq4Oi2UAAAxZWtk6OzvHxsYaFgYGBj50R7lcfvLkSS618PDwOHv27N///nfDkTmlUqlf29H5GCUQOjs7Dx8+vKCgwM/P78yZM9zyltTU1I0bNyYmJg4ZMkSn06lUqi5dupw7d+7FF18kovnz5587d27SpEmpqanPPfechYXFtWvX3nvvvYEDBx4/fjw/P/+9997r16/f3//+dyJqaGg4derU1q1bjdF5AABR4D/aKSELR0fHRoGwdVwGkpGRkZyczAVCuVzeo0ePLl269O/fv6amRiaT1dfXe3p6cvOFnZKxriPctm3bwYMHr1+/7ujoyOXp/fv35y4ZJKKvv/76559/tra2joqKGjlyJBG99dZbP/30U3JycklJCbeoqbKycsaMGVz73r179+7d29raunfv3rt27aqsrNyyZUu/fv2M1HkAgHYnYUnyaDOJ/9Vq+4KCgoyMDIVCcfLkyT59+nh7ex85cuStt966du3amDFj8vPztVptVVVVamrqd999R0Svv/76nj175s2bt2fPnhUrVgg/EtGTsJ3xTgSjgsZK8z3auxfikv9JeNPC23PjTd8TMA1c3iBmx5m9D22zekPSmbQ8Xh9bqyjVVh7PzMxstragoOD+/fvctpeXl7e3t06nKy8v9/LyIiKlUpmcnFxfX//EE0/oJ56uXLly//59qVQaERHBqycdC26xBgAgSm39YF4/Pz8/Pz/DEktLSy4KEpGDg0PT5YdDhgzh2YMOCYEQAECcWL6rRiV4+IQgCIQAAKLU1hkhtASPYQIAALOGjBAAQJSQEZoKAiEAgBgJewwTCIBAaI5w1YQY4PIGeAg8mNdUMEcIAABmDRkhAIAYSUz7GCZzhkAIACBKLBGDoVFTQCAEABAlZISmgjlCAAAwa8gIAQBECdcRmgoCIcD/gasaQCQkAu41ijlCQRAIAQBESUBGCIJgjhAAAMwaMkIAADGSsLyHRpFBCoNACAAgSiwRw3MXvu2BiBAIAQBEiuV/gTwWywiCOUIAADBryAjNReDyX//7Zm779UMQXNIA5gl3ljENBEIAAFES8BgmrJYRBIEQAECUcGcZU8EcIQAAmDVkhAAAYoRbrJkMAiEAgCgx/J9HyLc9EBECIfCC1ZsAJiMRtmpUYpzedGqYIwQAALOGjBAAQJRw+YSpIBACAIiSgECIoVFBEAgBAERJ2E23Md/FH84ZAACYNWSEAACixP95hLiOUBgEQnOEqyAAOgYjLJYpKyvz8PBotqqwsFCj0QQEBFhYWBCRUqm0tra2s7NjGObBgwddu3bl2ZkOA0OjAACixC2W4ftqWXJy8ubNm4cOHdps7Y4dO/Ly8tLS0iZOnFhRUUFEBw8edHd3DwkJiYiIKC8vN8oxigMyQgAAsxAVFRUZGfn+++83rfrtt99ycnLmz59PRBcvXvzggw8++ugjlmXT0tJ0Ol1ISIilpaXJ+2s6CIQAAKIkbNWoII6OjqWlpdy2l5fX1atXue2goKCGhobOHQUJQ6MAAOIkYVm+L/5zin8KDg7+7rvviIhl2aNHj86ZM4eIJBLJrl27rly5snz58uzs7LY8NpFBRggAIEos78UyWp36zp07kyZNMiwMDw9/9913H/ETvvzyy4iIiNmzZxNRTEyMVColIplMtnDhwtTUVF6d6UAQCAEAOgkrC1s3N7cVK1YYFra0RrSp9PT0urq6Dz74gHt74MCBGTNmSKVST0/Pixcv6nS6zjpGikAIACBKgoY6ZTLZxIkTH719XV2dvb09EeXn59+9e3fp0qVE9P333z/77LNffPFFZGSkVCqVy+W+vr6dNQoS5ggBAESKZYnh/2pZQUHB4cOHFQrFyZMnS0pKiOjw4cPh4eFEVFZWFhsbu3379okTJw4aNOjevXtEFBcXJ5FIGIaJj4//+OOPTXPQ7QIZIQCAufDx8TGc6psyZcqQIUOIyMbGZvv27fpyf39/Inr66adTUlLKysri4uL69Olj8s6aDgIhAIAo8V8s03p7Pz8/Pz8/wxJLS0svLy8icnFxafZC+8mTJ/PrQMeEQAgAIE4CHsOEe40KgUAIACBKQp5HiEAoBBbLAACAWUNGCAAgRhKWJK2uAm12FxAAgRAAQJQwNGoqCIQAAKKEQGgqmCMEAACzhowQAECskBGaBAIhAIAoPeyWac1AIBQEgRAAQJwwR2gimCMEAACzhowQAECUhNxr1Dg96ewQCAEARIlliGH47cK3PRARAiEAgEgJyAiREgqCOUIAADBryAgBAMSIZVmWZ0bItz1wEAgBAESJ5X8dId/2QEQIhAAAIsWyxPJc/IKMUBDMEQIAgFlDRggAIE64s4yJIBACAIgSw3/OD4FQEARCAABxYjBHaBqYIwQAALOGjBAAQJQEPIYJl08IgkAIACBGLCvgAnkEQiEQCAEARAk33TYVzBECAIBZQ0YIACBKQp5HiKFRIRAIAQBEScjQKAKhEAiEAACixH+xDIvFMoIYKxCWlpYeOXLExcXF2dl5/PjxjWpv3rx5+fJlGxub3r17Dxo0iIhUKtUPP/zg5eXV0NAwY8YMrtn+/futrKyqqqpiYmIcHR2JKCsrKzMz08rKql+/fqGhoUbqPAAAmA9jLZZZsGDBU089NWPGjAsXLqSlpRlW1dTUrFy58plnnpkzZ058fHxRURERLVmyZNKkSU888URDQ8N3331HRIcOHbp79+60adOmTZu2ZMkSIqqurl67du0zzzwzd+7crVu3lpaWGqnzAADtj3sME98X8GeUQJidnU1EXbp0IaLw8PDt27cb1h49ejQ4ONjCwoKI+vfvv2vXLpVKlZ6e7u/vT0Rjxoz5/PPPieirr7567LHHiMjZ2Tk/P7+oqOjQoUMhISESiYSIgoOD9+zZY4zOAwCIAvcYJr6vhykrK2up6t69ezdu3DAcj62trc3MzFSpVG1zRGJllEB49epVBwcHbtvBwSEzM9Ow9tq1azKZjNuWyWSZmZk5OTlWVlb6kmvXrnHN9B8ik8mysrKa7thSBxhcTAMAHRzLsizD99XaByYnJ2/evHno0KHN1m7evPnixYuWlpYrVqyor68nooyMjA0bNnTt2vXTTz/l0pvOyiiBUKFQ2NnZcdtdunR58OCBYW11dbWtra1hbXV1tWH7uro6tVpt2Mze3p5r1mjHljpw//79tj0iAIA2pNFoTP+PRkVFxcXFcUGukcrKysOHD0+fPj04OHjAgAHx8fFE9NZbb7366qvdu3dfunTp0qVLTd5f0zFKIJRKpfpUWqVSSaVSw1qZTFZXV2dYK5PJDNtbWVnZ2to226xRSUsd8PDwaNsjAgBoQ/rf9K0RMDRKAgfDzpw5061bN27bw8MjOTm5vr4+LS3Nzc2NiGQyWUZGRm1trbAPFz+jBEJ/f3+lUsltK5XKHj16GNb26NFDoVAY1vr5+dXU1OhL/Pz8JBJJ02ZNS4zReQAAcWC5+43yewlSXFysTy1kMtm9e/cqKiqsra31Dezt7cvLy9vgmETJKJdPjBo1qqamhmVZiUSSl5fHXQ5x6dKlmzdvPvfcc9OmTdNn2Xl5ec8884yHh0dQUFBNTY1MJsvNzeXaz549+/bt28OGDdPpdCzLDhw40NnZ+R//+Ae3461btxYuXNhSB+6q8n1H1GdnZ4eGhraSOAIRnTt3LiwszMbGpr07ImonT54cP348t1ALmqXValNTU8eNG9feHRE1lUp17dq1kSNHrlmz5t1332298dv7Xuf7+RcuXIiOjp40aZJhYXh4+EP/LZ1Op19aIZFINBqNVqtttNii2THVzsEogdDKyurdd9/dsWOHq6vrgwcPVqxYQUS1tbXcrJ63t/esWbP27dvX0NDQp0+fkSNHEtFnn322ffv2oKCg33777e233yaiv//975s2bTp27FhWVtbWrVslEom/v390dPT+/fvVavXgwYNbmvIlom3bttna2hYVFfn6+nLLU6Elc+bM6dmzZ3v3Quxwlh7FH3/8gbPUOpZl79696+/vb6Tpm2HDhn366ae+vr6GhY/yb7m5uemH8RQKRdeuXd3c3PQDdUSkVCq7du3atr0VDwn/x3wAAECHpNVqvb29DQc56+rq7O3t8/Pz4+Lijh07RkS7d+++cuXKv/71r8GDB587d04mk9XX14eEhOTl5bVfx40L2RIAgFkoKCj4+eefFQrFyZMnS0pKiOjw4cPcmFxgYKCXl1dBQQHDMCkpKYsWLSKiN954Y/fu3US0e/fulStXtm/njQoZIQCAWSgoKNBfWubl5eXt7c0wTHl5uaenJxFptdozZ87U1NQMHjzYz8+Pa5aRkVFeXi6VSiMiItqt38aHQAgAAGYNQ6MAAGDWzCIQGq59gpbgLAGAebJct25de/dBOLlcvn79erVanZiY2L17d2dn56ZttFrthAkT5s+fT0QNDQ3vvvtuTU3N8ePHdTpdo0XGnVVFRcUHH3ygVqsPHDjg6+vr5OTUtE1DQ8PEiRO5s1RQUDBkyJC0tLRvv/1WpVINGTLE5F1uB3l5eZ9//nltbe2ePXsGDx7c6MYfr7766qZNm5KTk3ft2jVmzBgHB4fKykr9WW3pu9f55OTkfPHFFzU1Nbt37x4yZEijy0+XLFny8ccfHzt2bNeuXePGjZPJZMeOHZs1a9a5c+e++eYbNze3wMDA9uq5KZ0+fTopKam8vDwpKWnkyJGNLj9Vq9UbN24sKSlJSUnx9PR0cXHJy8vbtm0bd1abfvfAFNiO7JVXXvntt99Ylq2trY2Ojm62zU8//eTm5sZtb9u27dtvv+W2J0yY0NDQYJp+tq9FixZlZGSwLKtUKqdOndpsm3379nXr1o3bzs/Pf+edd3bs2HH9+nXT9bK9RUdHV1VVsSx7/fr1xYsXN6r96KOPdu7cuXfvXpVKxZUsWbLk0qVLLMvW1ta2dFY7n8mTJysUCpZlr169unTp0ka1Gzdu3Llz5759++rq6riSgwcPbt++/ZtvvikoKDB1X9uJVqsdM2YMt7179+5///vfjRpMmzYtLy+PZdlFixYdOXKEZdkpU6Zw372srKy4uDjT9hdYlmU7diD08/Orrq7mtgMCAioqKho1yM3N/e2337y8vLi3U6ZMSUtL47ajo6PPnz9vsq62I29v79raWm7bz89PLpc3apCbm3vp0iX9WcrPzz958qRJu9jeqqqqevTowW3X1NR4eno2arB9+/ZGJb6+vlxIYFm2Z8+eTb97nU9lZWVAQAC3XVVV5ePj06hB07N08ODB0tJSU3RONH799deoqChu++LFi5GRkYa1Fy9eDAsLMyx58OCBv78/t61UKvX/G4IpGesJ9Sag1WqLior0d1Czt7cvKCgwvPcBwzDXrl2LjY3Vl/zxxx+GD3K6e/fu6NGjTdln06uvry8tLbW3t+fe2tvbFxUVubi46BswDHP9+vWZM2ca7nXq1KmampqcnJxJkyYNGjTIpD1uD4WFhYbPP7l//75ardaXEFFlZeW+ffusra2zs7PffPNNIioqKuKeuElE9vb2hYWFnfi+G5yCggL9F0kmk5WUlDQ0NBjejrKiooI7Szdu3HjzzTctLS2JKCkpydvb++rVqy+88IKPj0/7dN2E7ty5Y3jTzjt37hjWZmRkeHh47NmzRyKR3LhxY/Xq1YbfPalUWlZWptFoMDpqYh04EGo0GpZl9ePv1tbWjZZ7JCYmRkdHG5bU1dVx/3M2275Tqqurs7CwaOUs7d+/v9FZ8vT0XLx4saen54QJEwYPHpyZmWkYEjolwy+GRCKxtLSsra01POrY2NiAgAAiyszM/OyzzxYsWCCRSPR37zOf75L+LHFfKpVKZTjlPGfOHO4sXblyZdu2bUuWLBk+fLiDg4NUKvXz83vuuedOnTrVPl03Ie7/OG7b2tq60RMbysrKCgsLY2NjJRLJihUrvv766wEDBjT97iEQmlgHXjUqlUptbGz0z29SKpWGiU5+fr6dnV1DQ8ODBw8Yhnnw4IFWq3V1dTV8zIVh+87K0dGRiNRqNfe20VHfvn2bu3+S4VkqLi7mfvhLpdL6+vqsrKx26bkpGX4xuNsNGy5+0Wq11dXV3HZAQMCRI0dkMpmVlVVL373OyvAscceuf3Q2ETU0NOgfDsOdJSIqKyvjUsaAgIAzZ8504uf46LX+R8bT0zMoKIj7Yerj45OSkmLYXq1W63S6ZpezgVF14EBIRAMGDND/hdJqtb169dJXcT+sTpw4cfz4cblcfuLEiaqqKsP2CoViwIAB7dBp05JIJKGhofqjZlmW+83OsbS0VCqVJ06cSE5OrqqqOnHiRHV19RtvvKH/5V5bW2sO6yENb86uUCj69++v/5FORFlZWdx6WiLS50CG3yWGYcxhPaS/v79+W6FQhIaGGt7R/urVq/oHwujP0rPPPpubm8uV2NnZmUOiExoaanj36kZ/ZHr37q1/qGp9fb2TkxP31Dl9+5CQEMPvHphGxw6EL7300unTp4koKysrOjrazs6uuro6JCSEm3+OjY2NjY0dO3YswzDjx493c3NbsGDBmTNniOjBgweOjo7BwcHtfAAmoT9LGRkZ06ZNs7GxkcvlISEhCoWiZ8+e3FmKiIhgGCYyMrJr164vvPDCqFGjiOjMmTNjx44NCgpq5wMwPhsbm5iYmIyMDCI6efIk9wf92rVr3G2l+vbtu2zZMiJiGObw4cOvvfYaGZzVzMxM7rvXjv03DVtb26lTp3IjBPqzdOXKFe7RSyEhIa+88goR6XS6I0eOLF++nIjeeOMN7vvz008//b//9/+srDrwXMwj6tmzp4eHh1wuJ6JTp04tWLCAiPbv3//8888TUUREhFqt5iLlhQsXFi1aZGNjM3369KtXr5LBWQUT6/C3WDt48KCdnd29e/eefvppGxsblmWPHj0aHR3N/cgqLS09ePCgTCarqamZOXOmm5vbqVOnNBpNWVnZtGnTzGE4i4hYlj148KC9vf29e/eeeeYZa2tr7ixNnTqVa3Dv3r1Dhw5xZ2n27NkuLi6HDh1SKBQNDQ3PPvus4WqITqyhoSEpKUkmk1VXV8+dO5eIVCrVr7/+OmHCBCIqLCw8e/ZsTU3NiBEjBg8ezO2SlJTEnVXuu9eevTeV+vr6gwcPSqVSpVI5Z84cIqqtrb148eL48eOJqKCg4Ny5c0qlcuTIkQMHDuTaHzhwQKPR2NvbGy5b69yqq6uTk5Pt7Ozs7OwmT55MROXl5Xfu3BkxYgQRVVVV7d2718LCYuDAgcOGDaPmvntgYh0+EAIAAPwVHXtoFAAA4C9CIAQAALOGQAgAAGYNgRAAAMwaAiEAAJg1BEIAADBrCIQAAGDWEAgBAMCsIRACNK+4uPirr75qVJiXlxcREWEOz5oAMB8IhADN+/TTT5944olGhU5OTrm5uRUVFe3SJQAwBgRCgGYoFAo/P79u3bpxby9dusRteHh4/O1vf/Pz82u/rgFAG0MgBGjG8ePHZ8+ezW1nZ2d/8cUX+iofHx/Dxw8BQEeH/58BmlFQUODl5cVt37hxY+bMmdy2XC7HfeoBOhkEQoBmlJeX37p1i4gqKyvXr19fXl5ORDqdbtGiRc8880x79w4A2lLnf04mgADDhg2LjIyMiIhIT0/ftGnTvHnzjh49mpOTs3DhQg8Pj/buHQC0JTyPEKAZLMt++eWXd+7cef7554ODg8+ePXv48OEJEyZERUW1d9cAoI0hEAIAgFnDHCEAAJg1BEIAADBrCIQAAGDWEAgBAMCsIRACAIBZQyAEAACzhkAIAABmDYEQAADMGgIhAACYNQRCAAAwa/8fxUfHO9sw73MAAAAASUVORK5CYII=",
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      ]
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "cell_type": "code",
   "source": [
    "varied = (ω => range(0.4, 0.6, 100), F => range(1e-6, 0.01, 50))\n",
    "fixed = (α => 1.0, β => 2.0, ω0 => 1.0, γ => 0.01)\n",
    "\n",
    "result = get_steady_states(\n",
    "    harmonic_eq2, varied, fixed; threading=true, method=:total_degree\n",
    ")\n",
    "plot_phase_diagram(result; class=\"stable\")"
   ],
   "metadata": {},
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "source": [
    "---\n",
    "\n",
    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
   ],
   "metadata": {}
  }
 ],
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