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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# This notebook demonstrates some functionality of MuMoT when working with one-dimensional systems. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mumot\n",
    "\n",
    "mumot.__version__\n",
    "mumot.about()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## This model corresponds to the normal form of a pitchfork bifurcation in 1D  #######"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1 = mumot.parseModel(r\"\"\"\n",
    "\\emptyset + \\alpha_\\beta -> \\alpha_\\beta + \\alpha_\\beta : r\n",
    "\\alpha_\\beta + \\alpha_\\beta + \\alpha_\\beta -> \\emptyset + \\emptyset + \\emptyset : b\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1.showODEs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1.showMasterEquation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1.showVanKampenExpansion()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1.showFokkerPlanckEquation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1.showODEs(method='vanKampen')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1.showODEs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1.showNoiseEquations()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "model1.showNoiseSolutions()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mint1 = model1.integrate(initWidgets={'maxTime': [10,1,50,1]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mint1.showLogs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1.noiseCorrelations(initWidgets={'maxTime': [10,1,50,1]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "bif1 = model1.bifurcation('r', r'\\alpha_\\beta')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "bif1.showLogs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "mc1 = mumot.MuMoTmultiController([model1.integrate(params=[('b',2)], choose_yrange=[0,1], silent=True),\n",
    "                          model1.integrate(params=[('b',1)], choose_yrange=[0,1], silent=True)],\n",
    "                         shareAxes = False, silent=False);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mc1.showLogs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "mumot.MuMoTmultiController([model1.integrate(initWidgets={'maxTime':[10,5,50,1], \n",
    "                                               'initialState':{'\\\\alpha_\\\\beta': [0.3,0,1,0.01]}},\n",
    "                                           conserved=False, silent=True),\n",
    "                          model1.noiseCorrelations(initWidgets={'maxTime':[10,5,50,1], \n",
    "                                               'initialState':{'\\\\alpha_\\\\beta': [0.5,0,1,0.01]}},\n",
    "                                           conserved=False, silent=True)], shareAxes = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## This model is from van Kampen's book (1985, pp. 254), where analytical resultsare available for comparison (it works!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2 = mumot.parseModel(r\"\"\"\n",
    "(A) -> X : k\n",
    "X + X -> \\emptyset + \\emptyset : h\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2.showODEs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2.showODEs(method='vanKampen')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2.showMasterEquation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3 = model2.substitute('h = v, k = m')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3.showODEs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3.showODEs(method='vanKampen')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3.showNoiseEquations()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3.showNoiseSolutions()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2.integrate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3.integrate()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3.showStoichiometry()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2.showStoichiometry()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2.noiseCorrelations()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3.bifurcation('A','X')"
   ]
  }
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