{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Fisher-KPP equation\n",
    "\n",
    "We consider the Fisher-KPP equation\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial u}{\\partial t}=D\\frac{\\partial^2u}{\\partial{x}^2}+ru\\left(1-\\frac{u}{K}\\right),\n",
    "\\quad\\mbox{where}\\quad \n",
    "x\\in(-\\infty,+\\infty), \\quad t>0,\n",
    "\\end{equation}\n",
    "\n",
    "We non-dimensionalise using \n",
    "\n",
    "\\begin{equation}\n",
    "u=K\\tilde{u},\n",
    "\\qquad\n",
    "x=\\sqrt{\\frac{D}{r}}\\tilde{x},\n",
    "\\qquad\n",
    "t=\\frac{1}{r}\\tilde{t},\n",
    "\\end{equation}\n",
    "\n",
    "to give (dropping the tildes for notational convenience)\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\partial u}{\\partial t}=\\frac{\\partial^2u}{\\partial{x}^2}+u\\left(1-u\\right),\n",
    "\\quad\\mbox{where}\\quad \n",
    "x\\in(-\\infty,+\\infty), \\quad t>0.\n",
    "\\end{equation}\n",
    "\n",
    "To close the system, we specify initial and boundary conditions of the form\n",
    "\n",
    "\\begin{equation}\n",
    "u(x,0)=u_0(x)\n",
    "\\qquad\n",
    "u\\to{u_{\\pm\\infty}}\\text{ as }x\\to\\pm\\infty.\n",
    "\\end{equation}\n",
    "\n",
    "First we will solve the system numerically to investigate what the travelling wave might look like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import integrate\n",
    "from scipy import optimize\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "\n",
    "\n",
    "#set the plotting parameters\n",
    "plt.rcParams.update({\n",
    "    \"text.usetex\": True,\n",
    "    \"font.family\": \"serif\",\n",
    "    \"font.serif\": [\"Times New Roman\"],\n",
    "    \"font.size\": 18,\n",
    "    \"axes.linewidth\": 1.5,\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up the ODE system - discretised PDE using central differences \n",
    "def f(t,y,args):\n",
    "    \n",
    "    D,r,K,dx,n_odes=args\n",
    "    \n",
    "    derivs=np.zeros(n_odes)\n",
    "    \n",
    "    # convert the diffusion coefficient\n",
    "    d=D/dx**2\n",
    "    \n",
    "    derivs[0]=d*(-y[0]+y[1])+r*y[0]*(1.0-y[0]/K)  \n",
    "    # specify the derivatives\n",
    "    for ii in range(1,n_odes-1):\n",
    "                derivs[ii]=d*(y[ii-1]-2.0*y[ii]+y[ii+1])+r*y[ii]*(1.0-y[ii]/K)  \n",
    "    derivs[-1]=d*(y[-2]-y[-1])+r*y[-1]*(1.0-y[-1]/K)  \n",
    "    \n",
    "    return derivs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# model parameters\n",
    "\n",
    "L=150.0 # domain length\n",
    "dx=0.2 # spatial discretistion\n",
    "n_odes=int(L/dx)-1; # number of ODEs to solve\n",
    "xmesh=np.linspace(0,L,n_odes+2)\n",
    "\n",
    "t_final=100.0; # final time\n",
    "t=np.linspace(0,t_final,int(t_final)+1)\n",
    "dt=t[1]-t[0]\n",
    "\n",
    "D=1.0; # diffusion coefficient\n",
    "K=1.0; # carrying capacity\n",
    "r=1.0; # intrinsic growth rate\n",
    "\n",
    "args=[D,r,K,dx,n_odes]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initial conditions\n",
    "y0=np.zeros(n_odes)\n",
    "y0=0.5*(1.0-np.tanh(xmesh[1:-1]-10.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up the ODE solver\n",
    "y=np.empty((len(t),len(y0)),dtype=np.float)\n",
    "r=integrate.ode(f)\n",
    "r.set_integrator('dopri5');\n",
    "r.set_initial_value(y0,t[0]);\n",
    "r.set_f_params(args);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# solve the ODE\n",
    "idx=0\n",
    "while r.successful() and r.t<=t_final:\n",
    "    y[idx,:]=r.y\n",
    "    r.integrate(r.t+dt)\n",
    "    idx+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculate the solution at the left-hand and right-hand boundaries\n",
    "y_full=np.c_[y[:,0],y,y[:,-1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax=plt.subplots(figsize=(6,5))\n",
    "fig.tight_layout(pad=3.0)\n",
    "\n",
    "ax.plot(xmesh[1:-1],y0)\n",
    "ax.plot(xmesh,y_full[10,:])\n",
    "ax.plot(xmesh,y_full[20,:])\n",
    "ax.plot(xmesh,y_full[30,:])\n",
    "ax.plot(xmesh,y_full[40,:])\n",
    "ax.plot(xmesh,y_full[50,:])\n",
    "\n",
    "ax.set_xlabel(\"$x$\")\n",
    "ax.set_ylabel(\"$u(x,t)$\")\n",
    "ax.set_yticks(np.arange(0, 1.2, 0.2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Fisher-KPP travelling wave equation\n",
    "\n",
    "We consider the Fisher-KPP travelling wave equation\n",
    "\n",
    "\\begin{equation}\n",
    "\\frac{\\text{d}^2U}{\\text{d}z^2}+c\\frac{\\text{d}U}{\\text{d}z}+U(1-U)=0\n",
    "\\quad\\mbox{where}\\quad \n",
    "z\\in(-\\infty,+\\infty).\n",
    "\\end{equation}\n",
    "\n",
    "We convert to a system of first order ordinary differential equations in order to explore the phase plane:\n",
    "\n",
    "\\begin{eqnarray}\n",
    "\\frac{\\text{d}U}{\\text{d}z}&=&V;\\\\\n",
    "\\frac{\\text{d}^V}{\\text{d}z}&=&-cV-U(1-U).\n",
    "\\end{eqnarray}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up the ODE system for the phase plane\n",
    "def pp(t,y,args):\n",
    "    \n",
    "    c=args\n",
    "    \n",
    "    derivs=np.zeros(2)\n",
    "    \n",
    "    derivs[0]=y[1]\n",
    "    derivs[1]=-c*y[1]-y[0]*(1.0-y[0])\n",
    "    \n",
    "    return derivs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# model parameters\n",
    "c=2.0;\n",
    "tpp_final=1e4; # final time\n",
    "tpp=np.linspace(0,tpp_final,10*int(tpp_final)+1)\n",
    "dtpp=tpp[1]-tpp[0]\n",
    "args=c\n",
    "\n",
    "# initial conditions\n",
    "ypp0=[0.999,-0.001]\n",
    "\n",
    "# set up the ODE solver\n",
    "y_pp=np.empty((len(tpp),len(ypp0)),dtype=np.float)\n",
    "r=integrate.ode(pp)\n",
    "r.set_integrator('dopri5');\n",
    "r.set_initial_value(ypp0,tpp[0]);\n",
    "r.set_f_params(args);\n",
    "\n",
    "# solve the ODE\n",
    "idx=0\n",
    "while r.successful() and r.t<=tpp_final:\n",
    "    y_pp[idx,:]=r.y\n",
    "    r.integrate(r.t+dtpp)\n",
    "    idx+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the results\n",
    "fig,ax=plt.subplots(figsize=(6,5))\n",
    "\n",
    "# create a quiver plot to see where the trajectory directions\n",
    "x,y=np.meshgrid(np.arange(0,1.06,0.025),np.arange(-0.16,0.06,0.025))\n",
    "u=y\n",
    "v=-c*y-x*(1.0-x)\n",
    "n=-2\n",
    "color=np.sqrt(((u-n)/2)**2+((v-n)/2)**2) \n",
    "ax.quiver(x,y,u,v,color,width=0.002)\n",
    "\n",
    "# plot a trajectory that starts very close to the unstable fixed point\n",
    "ax.plot(y_pp[:,0],y_pp[:,1])\n",
    "\n",
    "# plot the null clines and the y axis\n",
    "xplot=np.arange(-0.05,1.1,0.005)\n",
    "yplot=np.arange(-0.16,0.1,0.05)\n",
    "ax.plot(xplot,-1/c*xplot*(1-xplot),color='black',linestyle='--');\n",
    "ax.plot(xplot,np.zeros(len(xplot)),color='black',linestyle=':');\n",
    "ax.plot(np.zeros(len(yplot)),yplot,color='black')\n",
    "\n",
    "ax.set_xlabel(\"$U$\")\n",
    "ax.set_ylabel(\"$V=U'$\")\n",
    "ax.set_xlim(-0.05,1.05)\n",
    "ax.set_ylim(-0.15,0.05)\n",
    "ax.set_yticks(np.arange(-0.15, 0.1, 0.05));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot and save both figures together\n",
    "\n",
    "fig,ax=plt.subplots(1,2,figsize=(12,5))\n",
    "fig.tight_layout(pad=3.0)\n",
    "\n",
    "# travelling waves\n",
    "ax[0].plot(xmesh[1:-1],y0)\n",
    "ax[0].plot(xmesh,y_full[10,:])\n",
    "ax[0].plot(xmesh,y_full[20,:])\n",
    "ax[0].plot(xmesh,y_full[30,:])\n",
    "ax[0].plot(xmesh,y_full[40,:])\n",
    "ax[0].plot(xmesh,y_full[50,:])\n",
    "ax[0].set_xlabel(\"$x$\")\n",
    "ax[0].set_ylabel(\"$u(x,t)$\")\n",
    "ax[0].set_yticks(np.arange(0, 1.2, 0.2))\n",
    "\n",
    "# phase plane\n",
    "# create a quiver plot to see where the trajectory directions\n",
    "x,y=np.meshgrid(np.arange(0,1.06,0.025),np.arange(-0.16,0.06,0.025))\n",
    "u=y\n",
    "v=-c*y-x*(1.0-x)\n",
    "n=-2\n",
    "color=np.sqrt(((u-n)/2)**2+((v-n)/2)**2) \n",
    "ax[1].quiver(x,y,u,v,color,width=0.002)\n",
    "# plot a trajectory that starts very close to the unstable fixed point\n",
    "ax[1].plot(y_pp[:,0],y_pp[:,1])\n",
    "# plot the null clines and the y axis\n",
    "xplot=np.arange(-0.05,1.1,0.005)\n",
    "yplot=np.arange(-0.16,0.1,0.05)\n",
    "ax[1].plot(xplot,-1/c*xplot*(1-xplot),color='black',linestyle='--');\n",
    "ax[1].plot(xplot,np.zeros(len(xplot)),color='black',linestyle=':');\n",
    "ax[1].plot(np.zeros(len(yplot)),yplot,color='black')\n",
    "ax[1].set_xlabel(\"$U$\")\n",
    "ax[1].set_ylabel(\"$V=U'$\")\n",
    "ax[1].set_xlim(-0.05,1.05)\n",
    "ax[1].set_ylim(-0.15,0.05)\n",
    "ax[1].set_yticks(np.arange(-0.15, 0.1, 0.05))\n",
    "\n",
    "# to save the figure\n",
    "# outputpath='../Lecture Notes/Chapter_TravellingWaves/figures/Fisher_KPP.pdf'\n",
    "# plt.savefig(outputpath,bbox_inches=\"tight\", pad_inches=0.1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
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