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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MuMoT test notebook for using letters from the Greek alphabet"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook tests some basic functionality of MuMoT when reactants and rates are Greek letters (with Greek indices). The analysis is based on the honeybee stop-signal model (Seeley et al. (2012) & Pais et al. (2013)) studied in more detail in the user manual. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import mumot\n",
    "\n",
    "mumot.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model1 = mumot.parseModel(r\"\"\"\n",
    "U -> \\alpha : g_1\n",
    "U -> \\Gamma_\\beta : g_2\n",
    "\\alpha -> U : a_1\n",
    "\\Gamma_\\beta -> U : a_2\n",
    "\\alpha + U -> \\alpha + \\alpha : r_1\n",
    "\\Gamma_\\beta + U -> \\Gamma_\\beta + \\Gamma_\\beta : r_2\n",
    "\\alpha + \\Gamma_\\beta -> \\alpha + U : \\sigma\n",
    "\\alpha + \\Gamma_\\beta -> \\Gamma_\\beta + U : \\sigma\n",
    "\"\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "int1 = model1.integrate(showStateVars=['\\\\alpha', '\\\\Gamma_\\\\beta', 'U'],\n",
    "                        initWidgets={'maxTime':[10,5,50,1], \n",
    "                                     'initialState':{'U': [0.5,0,1,0.01],'\\\\Gamma_\\\\beta': [0.5,0,1,0.1],'\\\\alpha': [0,0,1,0.1]},\n",
    "                                    'g_{1}':[0.5,0,1,0.01]},\n",
    "        \n",
    "                       conserved=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "int1.showLogs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2 = model1.substitute('a_1 = 1/v_1, a_2 = 1/v_2, g_1 = v_1, g_2 = v_2, r_1 = v_1, r_2 = v_2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3 = model2.substitute('v_1 = \\\\mu + \\\\Delta/2, v_2 = \\\\mu - \\\\Delta/2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3.showODEs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model3.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model4 = model3.substitute('U = N - \\\\alpha - \\\\Gamma_\\\\beta')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "modelBifCont1 = model4.bifurcation('\\\\sigma','\\\\alpha-\\\\Gamma_\\\\beta', \n",
    "                                   initWidgets={'mu':[3, 1, 5, 0.5], 'Delta':[0, 0, 2, 0.1], \n",
    "                                                'initBifParam':[4.8, 3, 5, 0.1]},\n",
    "                                   choose_xrange=[0, 5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "modelStreamCont1 = model4.stream('\\\\alpha', '\\\\Gamma_\\\\beta',fontsize=25, xlab=r'this is the x-label', \n",
    "                                 showFixedPoints=False, showNoise=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model4.SSA()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model4.showODEs(method='vanKampen')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model4.showMasterEquation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "model4.showFokkerPlanckEquation()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "model4.showVanKampenExpansion()"
   ]
  }
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