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 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# This notebook provides a quick test for bifurcation plots in MuMoT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mumot\n",
    "\n",
    "mumot.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%model\n",
    "$\n",
    "U -> A : g_A\n",
    "U -> B : g_B\n",
    "A -> U : a_A\n",
    "B -> U : a_B\n",
    "A + U -> A + A : r_A\n",
    "B + U -> B + B : r_B\n",
    "A + B -> A + U : s\n",
    "A + B -> B + U : s\n",
    "$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1 = mumot.parseModel(In[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2 = model1.substitute('U = N - A - B')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3 = model2.substitute('a_A = 1/v_A, a_B = 1/v_B, g_A = v_A, g_B = v_B, r_A = v_A, r_B = v_B')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model4 = model3.substitute('v_A = \\mu + \\Delta/2, v_B = \\mu - \\Delta/2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "bifurcation1 = model4.bifurcation('s','A-B', choose_xrange = [0,5], initWidgets={'initBifParam': [4.5,0,5,0.1]})\n",
    "# to get started, here is a parameter combination that works\n",
    "# set \\mu = 3\n",
    "# set \\Delta = 0.1 for unfolding of pitchfork\n",
    "# set \\Delta = 0 for pitchfork"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "bifurcation1.showLogs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "bifurcation2 = model4.bifurcation('\\\\Delta','A-B', initBifParam = 2.0, params = [('\\\\mu', 4), ('s', 4)], \n",
    "                                  choose_xrange = [-2,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "bifurcation2.showLogs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "multiController4 = mumot.MuMoTmultiController([model4.bifurcation('s','A', silent = True), \n",
    "                                             model4.bifurcation('s','B', silent = True)], \n",
    "                                            shareAxes = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "multiController4.showLogs()"
   ]
  }
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