{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5b1364fc-3526-42ec-ac46-795341e5f643",
   "metadata": {},
   "source": [
    "# Population "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "3cb66c1b-bfe9-4660-a69d-858c19afb39f",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import sympy as sp\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "514657eb-f78b-4ca6-b1e1-d121960c7e58",
   "metadata": {},
   "outputs": [],
   "source": [
    "run = \"stable\"\n",
    "# run = \"unstable\"\n",
    "# run = \"no interaction\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "659040cf-c802-4fd3-bee1-163885665409",
   "metadata": {},
   "source": [
    "## Define initial population and equilibrium"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "c337e4b7-5cf5-4c93-a5ff-b2698408fb9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define initial population\n",
    "if run==\"stable\":\n",
    "    u0 = np.array([100, 70, 30])\n",
    "    equilibrium = np.array([925/9, 250/3, 895/36])\n",
    "elif run==\"unstable\":\n",
    "    u0 = np.array([103, 83, 427])  # very cloze to equilibrium already\n",
    "    equilibrium = np.array([925/9, 250/3, 11540/27])\n",
    "elif run==\"no interaction\":\n",
    "    u0 = np.array([100, 70, 30])\n",
    "    equilibrium = np.array([350/3, 0, 0])\n",
    "else:\n",
    "    raise ValueError(f\"Unknown mode {run}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "21d51d0a-5294-47bc-9b2c-633f28aea257",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([100,  70,  30])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "0a9a4f0e-ffe9-402e-b3e0-bda4bfd16d75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([102.77777778,  83.33333333,  24.86111111])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "equilibrium"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5fb2677-badb-4fbf-bc80-fb3889f30ae1",
   "metadata": {},
   "source": [
    "## Define non-linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "6c8eb9c6-4e22-44e0-9079-3d182b2e0cf6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define parameters\n",
    "if run==\"stable\":\n",
    "    parameters = np.array([\n",
    "        [1.7, -0.006, -0.001],\n",
    "        [0.99, 0.003,-0.012],\n",
    "        [0.975, 0.0003, np.nan]\n",
    "    ])\n",
    "elif run==\"unstable\":\n",
    "    parameters = np.array([\n",
    "        [1.7, -0.006, -0.001],\n",
    "        [0.99, 0.05,-0.012],  # here we use a larger valuee 0.05 instead of 0.003\n",
    "        [0.975, 0.0003, np.nan]\n",
    "    ])\n",
    "elif run==\"no interaction\":\n",
    "    parameters = np.array([\n",
    "        [1.7, -0.006, 0],\n",
    "        [0.99, 0,0],  # here we use a larger valuee 0.05 instead of 0.003\n",
    "        [0.975, 0, np.nan]\n",
    "    ])\n",
    "else:\n",
    "    raise ValueError(f\"Unknown mode {run}\")\n",
    "\n",
    "def u_new(u_old, parameters):\n",
    "    return np.array([\n",
    "        parameters[0, 0]*u_old[0]+parameters[0, 1]*u_old[0]**2+parameters[0, 2]*u_old[0]*u_old[1],\n",
    "        parameters[1, 0]*u_old[1]+parameters[1, 1]*u_old[0]*u_old[1]+parameters[1, 2]*u_old[1]*u_old[2],\n",
    "        parameters[2, 0]*u_old[2]+parameters[2, 1]*u_old[1]*u_old[2]]\n",
    "                   )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "5147a612-fff0-467b-be84-ad8d4279add0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([103.  ,  65.1 ,  29.88])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_new(u0, parameters)  # We comput u1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "0b7c0e81-0eca-4997-9698-ae445fa8763e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([102.77777778,  83.33333333,  24.86111111])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_new(equilibrium, parameters)  # No change at equilibrium"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "29eaf548-92a8-4933-acb7-23fe42f60bfc",
   "metadata": {},
   "source": [
    "## Evaluate the non-linear model and visualize it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "58ac3125-94a5-448a-b433-56a27b3aa7dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1600x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Time = 200  # Max value for timee variable\n",
    "\n",
    "# Apply the non-linear model\n",
    "U = np.zeros((Time+1, 3))\n",
    "U[0] = u0\n",
    "for t in range(Time):\n",
    "    U[t+1] = u_new(U[t], parameters)\n",
    "\n",
    "# Plot everything\n",
    "time = np.arange(Time+1)\n",
    "\n",
    "plt.figure(figsize=(16, 4.5))\n",
    "\n",
    "plt.plot(time, U[:,0], label=\"plants\")\n",
    "plt.plot(time, U[:,1], label=\"rabbits\")\n",
    "plt.plot(time, U[:,2], label=\"foxes\")\n",
    "\n",
    "#plt.hlines(equilibrium[0], 0, Time, linestyles=\"dashed\", linewidth=1, label=\"plants equilibrium\")\n",
    "#plt.hlines(equilibrium[1], 0, Time, linestyles=\"dashed\", linewidth=1, label=\"rabbits equilibrium\")\n",
    "#plt.hlines(equilibrium[2], 0, Time, linestyles=\"dashed\", linewidth=1, label=\"foxes equilibrium\")\n",
    "\n",
    "plt.xlabel(\"time\")\n",
    "plt.ylabel(\"population\")\n",
    "plt.title(\"Non-Linear Model\")\n",
    "plt.legend(loc=\"right\")\n",
    "plt.grid(True, alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11df367e-864b-4e95-bc2b-ed8d907f9571",
   "metadata": {},
   "source": [
    "## Define linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "49a40c04-1df5-4af4-9c22-0aa807fa3d70",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define matrix\n",
    "if run==\"stable\":\n",
    "    A = np.array([\n",
    "        [0.38333333, -0.10277778, 0.],\n",
    "        [0.25, 1. , -1.],\n",
    "        [0., 0.00745833, 1.]\n",
    "    ])\n",
    "elif run==\"unstable\":\n",
    "    A = np.array([\n",
    "        [0.03333333, -0.01611111, 0.],\n",
    "        [0.1, 1., -0.4],\n",
    "        [0., 0.02620833, 1.]\n",
    "    ])\n",
    "elif run==\"no interaction\":\n",
    "    A = np.array([\n",
    "        [0.3 ,0., 0.],\n",
    "        [0., 0.99, 0.],\n",
    "        [0., 0., 0.975]\n",
    "    ])\n",
    "else:\n",
    "    raise ValueError(f\"Unknown mode {run}\")\n",
    "\n",
    "\n",
    "def u_new_linear(u_old, A, equilibrium):\n",
    "    return equilibrium + np.matmul(A, u_old - equilibrium)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "38c90279-c521-469e-9166-7a1f796b2678",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([103.08333337,  64.16666667,  29.9005556 ])"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_new_linear(u0, A, equilibrium)  # We compute u1 for the linear model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "b9b332ea-ada7-4d35-9514-fae67bdb5bde",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([102.77777778,  83.33333333,  24.86111111])"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u_new_linear(equilibrium, A, equilibrium)  # No change at equilibrium"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c72619a8-13bc-4683-89ce-cea7891153be",
   "metadata": {},
   "source": [
    "# Evaluate the linear model and visualize it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "b686938e-6dc3-418c-ba4c-4165390f7d27",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1600x450 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "U_linear = np.zeros((Time+1, 3))\n",
    "U_linear[0] = u0\n",
    "\n",
    "for t in range(Time):\n",
    "    U_linear[t+1] = u_new_linear(U_linear[t], A, equilibrium)\n",
    "\n",
    "# Plot everything\n",
    "plt.figure(figsize=(16, 4.5))\n",
    "\n",
    "plt.plot(time, U[:,0], label=\"plants\")\n",
    "plt.plot(time, U[:,1], label=\"rabbits\")\n",
    "plt.plot(time, U[:,2], label=\"foxes\")\n",
    "\n",
    "plt.plot(time, U_linear[:,0], label=\"plants_linear\")\n",
    "plt.plot(time, U_linear[:,1], label=\"rabbits_linear\")\n",
    "plt.plot(time, U_linear[:,2], label=\"foxes_linear\")\n",
    "\n",
    "plt.hlines(equilibrium[0], 0, Time, linestyles=\"dashed\", linewidth=1, label=\"plants equilibrium\")\n",
    "plt.hlines(equilibrium[1], 0, Time, linestyles=\"dashed\", linewidth=1, label=\"rabbits equilibrium\")\n",
    "plt.hlines(equilibrium[2], 0, Time, linestyles=\"dashed\", linewidth=1, label=\"foxes equilibrium\")\n",
    "\n",
    "plt.xlabel(\"time\")\n",
    "plt.ylabel(\"population\")\n",
    "plt.title(\"Non-Linear and Linear Model\")\n",
    "plt.legend(loc=\"right\")\n",
    "plt.grid(True, alpha=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7b09420-3b91-4a20-bc6c-bcb356127b2a",
   "metadata": {},
   "source": [
    "We see that linear model is very similar to non-linear model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a597445-bbbe-4d1e-931f-455539ca9fda",
   "metadata": {},
   "source": [
    "## Compute all eigenvalues, eigenvectors and the decomposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "f54c342b-97f0-4a03-94c8-aad15ee85275",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.42719344+0.j        , 0.97806995+0.08688205j,\n",
       "       0.97806995-0.08688205j])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eigenvalues, eigenvectors = np.linalg.eig(A)\n",
    "eigenvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "6d03e532-90e1-4c2f-b622-98198874058a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.42719344, 0.98192124, 0.98192124])"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.abs(eigenvalues)  # All eigenvalues have absolute value less than 1 if run==\"stable\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "3a34f688-d778-4eb3-b7eb-1c51c0911949",
   "metadata": {},
   "outputs": [],
   "source": [
    "D = np.diag(eigenvalues)\n",
    "T = eigenvectors\n",
    "T_inv = np.linalg.inv(T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "cf3f2527-1133-44a0-8a53-86c921fdda6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.08859756, -0.08859756])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.angle(eigenvalues)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da475ba2-3395-4859-9330-a363bf8425dd",
   "metadata": {},
   "source": [
    "## Define linear model again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "a6a65685-da06-48ad-b536-e8e860f0539a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_model(u0, T, eigenvalues, T_inv, equilibrium, t):\n",
    "    # We want to allow t to be infinity i.e. np.inf or sp.oo\n",
    "    # Therefore we have an if-else construct\n",
    "    if t in (np.inf, sp.oo):\n",
    "        time = sp.symbols(\"time\", integer=True, positive=True)\n",
    "        eigenvalues_mod = np.array([sp.limit(element**time, time, sp.oo) for element in eigenvalues])\n",
    "    else:\n",
    "        eigenvalues_mod = eigenvalues**t\n",
    "    D_mod = np.diag(eigenvalues_mod)\n",
    "    u_t = np.matmul(T_inv, u0 - equilibrium)\n",
    "    u_t = np.matmul(D_mod, u_t)\n",
    "    u_t = np.matmul(T, u_t)\n",
    "    u_t = equilibrium + u_t\n",
    "    u_t = np.real(u_t)  # To avoid small imaginary rounding errors\n",
    "    return u_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "14b4f01b-1b87-4e8d-8a48-d531a84fd555",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([107.71288299,  47.4751713 ,  29.12338404])"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use u_new_linear to get u_5\n",
    "u1 = u_new_linear(u0, A, equilibrium)\n",
    "u2 = u_new_linear(u1, A, equilibrium)\n",
    "u3 = u_new_linear(u2, A, equilibrium)\n",
    "u4 = u_new_linear(u3, A, equilibrium)\n",
    "u5 = u_new_linear(u4, A, equilibrium)\n",
    "u5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "653847cf-afa6-4b6d-86e4-30ae817a1c72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([107.71288299,  47.4751713 ,  29.12338404])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Or use linear_population_model once\n",
    "linear_model(u0, T, eigenvalues, T_inv, equilibrium, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "99232895-2fdf-4b48-8729-a7fada09e59f",
   "metadata": {},
   "source": [
    "We see that both models are equivalent"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ade5036a-5a13-40aa-a851-b77f51db45a3",
   "metadata": {},
   "source": [
    "## Time to infinity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "ed31a506-9ce1-4e63-a16a-2e8700926645",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([102.77777778,  83.33333333,  24.86111111])"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "equilibrium"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "545789a6-4bb0-4549-a819-7573e482bcb9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([102.49181627,  84.91541611,  24.88674436])"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For the non-linear model we have to use the for loop from above to get e.g.\n",
    "U[200]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "7c973db2-906b-4e76-b107-b0d450fa16b0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([102.54109969,  84.58311219,  24.91797488])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For the first linear model we have to use the for loop from above to get e.g.\n",
    "U_linear[200]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "6c3727a2-bb9c-4932-a7e6-054718200cad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([102.54109969,  84.58311219,  24.91797488])"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For the second linear model we can directly insert t=200 to get the same as U_linear[200]\n",
    "linear_model(u0, T, eigenvalues, T_inv, equilibrium, 200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "695c0479-5425-430d-ac1a-3dbf8a978a4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([102.77777786,  83.33333276,  24.86111116])"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# For the second linear model we can directly insert a larger value e.g. t=1000\n",
    "linear_model(u0, T, eigenvalues, T_inv, equilibrium, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "20d1b9fa-49d1-4f72-97e9-e95ec14750b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([102.777777777778, 83.3333333333333, 24.8611111111111], dtype=object)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Or we can use t=inf\n",
    "linear_model(u0, T, eigenvalues, T_inv, equilibrium, np.inf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8e00791a-d1d9-4208-872b-20756c19c391",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "41c29b7e-2006-4eb8-b73d-227b96e46d3c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "551650f5-0b2d-4866-8511-fe1e8c73b8e7",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1d2da17d-6766-4a47-8377-812c5ab3b7bd",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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