{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "c6805951",
   "metadata": {},
   "source": [
    "# Multidimensional differential equations\n",
    "\n",
    "- Börge Göbel "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "921259c3",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "from scipy import integrate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29eb17ec",
   "metadata": {},
   "source": [
    "## Lorenz system"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b461fb52",
   "metadata": {},
   "source": [
    "We solve the three coupled differential equations\n",
    "\n",
    "\\\\( \n",
    "\\dot{x} = a(y-x)\\\\\n",
    "\\dot{y} = x(b-z)-y\\\\\n",
    "\\dot{z} = xy-cz\\\\\n",
    "\\\\)\n",
    "\n",
    "Here \\\\( x,y,z \\\\) are the coordinates and \\\\( a,b,c \\\\) are coefficients"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3b00b9ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f_ODE(t,r,a,b,c):\n",
    "    x,y,z = r\n",
    "    x1 = a*(y-x)\n",
    "    y1 = x*(b-z)-y\n",
    "    z1 = x*y-c*z\n",
    "    return [x1,y1,z1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7493e05",
   "metadata": {},
   "source": [
    "### Chaotic solution: For b > 24.74, two repulsive points exist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d939c8b7",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 10.0\n",
    "b = 50.0\n",
    "c = 8.0/3.0\n",
    "\n",
    "tStart = 0\n",
    "tEnd = 50\n",
    "\n",
    "x0 = 1.0\n",
    "y0 = 0.0\n",
    "z0 = 0.0\n",
    "\n",
    "solution = integrate.solve_ivp(f_ODE, [tStart, tEnd], [x0, y0, z0], method='RK45', t_eval=np.linspace(tStart,tEnd,5001), args=(a,b,c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "3ff6c7c7",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<mpl_toolkits.mplot3d.art3d.Line3D at 0x22bb78264f0>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plottrajectory = plt.axes(projection='3d')\n",
    "plottrajectory.plot3D(solution.y[0],solution.y[1],solution.y[2], linewidth=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "1e25185b",
   "metadata": {},
   "outputs": [],
   "source": [
    "solution2 = integrate.solve_ivp(f_ODE, [tStart, tEnd], [1.1*x0, y0, z0], method='RK45', t_eval=np.linspace(tStart,tEnd,5001), args=(a,b,c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "77e1618d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plottrajectory = plt.axes(projection='3d')\n",
    "plottrajectory.plot3D(solution.y[0],solution.y[1],solution.y[2], linewidth=0.5)\n",
    "plottrajectory.plot3D(solution2.y[0],solution2.y[1],solution2.y[2], linewidth=0.5)\n",
    "plt.savefig('Lorenz_trajectory.png',dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7338ce52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10.74272658, 21.0668307 , 31.29407404])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution.y[:,-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e081b3e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-11.78604861, -17.41325428,  44.25937873])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution2.y[:,-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "315e1f0b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x22bb91a1070>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(solution.t, solution.y[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1687415c",
   "metadata": {},
   "source": [
    "### Non-chaotic solution: For b < 24.74, the two points become attractive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "a0493a73",
   "metadata": {},
   "outputs": [],
   "source": [
    "a = 10.0\n",
    "b = 20.0\n",
    "c = 8.0/3.0\n",
    "\n",
    "tStart = 0\n",
    "tEnd = 50\n",
    "\n",
    "x0 = 1.0\n",
    "y0 = 0.0\n",
    "z0 = 0.0\n",
    "\n",
    "solution = integrate.solve_ivp(f_ODE, [tStart, tEnd], [x0, y0, z0], method='RK45', t_eval=np.linspace(tStart,tEnd,5001), args=(a,b,c))\n",
    "solution2 = integrate.solve_ivp(f_ODE, [tStart, tEnd], [1.1*x0, y0, z0], method='RK45', t_eval=np.linspace(tStart,tEnd,5001), args=(a,b,c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "20638182",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plottrajectory = plt.axes(projection='3d')\n",
    "plottrajectory.plot3D(solution.y[0],solution.y[1],solution.y[2], linewidth=0.5)\n",
    "plottrajectory.plot3D(solution2.y[0],solution2.y[1],solution2.y[2], linewidth=0.5)\n",
    "plt.savefig('Lorenz_trajectory2.png',dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "17b75614",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
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