Predator_Prey_Control_Ex.ipynb

environment.yml

channels:
  - defaults
dependencies:
  - ipython
  - numpy
  - scipy
  - matplotlib
  - notebook
  - console_shortcut
  - ipywidgets

Predator_Prey_Control_Ex.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "01d7bb8c",
   "metadata": {
    "pycharm": {
     "is_executing": true
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import solve_ivp\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interact, widgets, Layout\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7c4824de",
   "metadata": {},
   "outputs": [],
   "source": [
    "def u(t):\n",
    "    if 0<= t <= 2:\n",
    "        return 0\n",
    "    elif 2< t <= 4.5:\n",
    "        return 1\n",
    "    elif 4.5< t <=7.5:\n",
    "        return 0.5\n",
    "    else:\n",
    "        return 0\n",
    "vu = np.vectorize(u,otypes=[np.float64])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "9fe85e13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "7390ef4846d542458bfacfaad4225c01",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=0.5, description='Initial Prey Population $\\\\quad$', layout=Layout(wid…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def model_control_ex(t,x):\n",
    "    return np.array([x[0]-x[0]*x[1]-0.4*x[0]*u(t), -x[1]+x[0]*x[1]-0.2*x[1]*u(t)])\n",
    "def plot_pp(a,b):\n",
    "    t0 = 0\n",
    "    tmax = 12\n",
    "    sol = solve_ivp(lambda t, x:model_control_ex(t,x), [t0, tmax], np.array([a,b]), t_eval=np.linspace(t0, tmax, 100))\n",
    "    plt.subplot(1,2,1)\n",
    "    plt.plot(sol.t,sol.y[0], label = 'Prey')\n",
    "    plt.plot(sol.t,sol.y[1], label = 'Predator')\n",
    "    plt.xlabel(\"time\")\n",
    "    plt.ylabel(\"population\")\n",
    "    plt.title(\"Solution of the ODE system\")\n",
    "    plt.legend()\n",
    "    plt.subplot(1,2,2)\n",
    "    plt.plot(sol.y[1],sol.y[0], label = 'Prey', color = \"r\")\n",
    "    plt.rcParams[\"figure.figsize\"]=10,5\n",
    "    plt.title(\"Phase portrait of the solution\")\n",
    "    plt.xlabel(\"predator population\")\n",
    "    plt.ylabel(\"prey population\")\n",
    "\n",
    "style = {'description_width': 'initial'}\n",
    "layout = Layout(width = \"400px\")\n",
    "slid1 = widgets.FloatSlider(description = 'Initial Prey Population $\\quad$',min=0, max=1, step=0.1, value=0.5,style = style, layout = layout)\n",
    "slid2 = widgets.FloatSlider(description = 'Initial Predator Population',min=0, max=1, step=0.1, value=0.7, style = style, layout = layout)\n",
    "interact(plot_pp, a= slid1 ,b=slid2);"
   ]
  }
 ],
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