github_readme.ipynb

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     "text": [
      "\r",
      "\u001b[32mTracking 9 paths... 100%|███████████████████████████████| Time: 0:00:16\u001b[39m\r\n",
      "\u001b[34m  # paths tracked:                  9\u001b[39m\r\n",
      "\u001b[34m  # non-singular solutions (real):  3 (0)\u001b[39m\r\n",
      "\u001b[34m  # singular endpoints (real):      0 (0)\u001b[39m\r\n",
      "\u001b[34m  # total solutions (real):         3 (0)\u001b[39m\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "A steady state result for 100 parameter points\n",
       "\n",
       "Solution branches:   3\n",
       "   of which real:    3\n",
       "   of which stable:  2\n",
       "\n",
       "Classes: stable, physical, Hopf, binary_labels\n"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using HarmonicBalance\n",
    "@variables α, ω, ω0, F, t, η, x(t) # declare constant variables and a function x(t)\n",
    "diff_eq = DifferentialEquation(d(x,t,2) + ω0^2*x + α*x^3 + η*d(x,t)*x^2 ~ F*cos(ω*t), x)\n",
    "add_harmonic!(diff_eq, x, ω) # specify the ansatz x = u(T) cos(ωt) + v(T) sin(ωt)\n",
    "\n",
    "# implement ansatz to get harmonic equations\n",
    "harmonic_eq = get_harmonic_equations(diff_eq)\n",
    "\n",
    "fixed = (α => 1., ω0 => 1.0, F => 0.01, η=>0.1)   # fixed parameters\n",
    "varied = ω => LinRange(0.9, 1.2, 100)           # range of parameter values\n",
    "result = get_steady_states(harmonic_eq, varied, fixed)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a76a34ed",
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      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(result, \"sqrt(u1^2 + v1^2)\", size=(380,280))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "dd79b9e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "savefig(\"github_readme_plot.png\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "04ef17c1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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