{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Low-dimensional Analyzers"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"@[Chaoming Wang](https://github.com/chaoming0625)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have talked about model [simulation](../tutorial_simulation/index.rst) and [training](../tutorial_training/index.rst) for dynamical systems with BrainPy. In this tutorial, we are going to dive into how to perform automatic analysis for your defined systems. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As is known to us all, dynamics analysis is necessary in neurodynamics. This is because blind simulation of nonlinear systems is likely to produce few results or misleading results. BrainPy has well supports for low-dimensional systems, no matter how nonlinear your defined system is. Specifically, BrainPy provides the following methods for the analysis of low-dimensional systems:\n",
"\n",
"1. phase plane analysis;\n",
"2. codimension 1 or codimension 2 bifurcation analysis;\n",
"3. bifurcation analysis of the fast-slow system. \n",
"\n",
"BrainPy will help you probe the dynamical mechanism of your defined systems rapidly. "
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"ExecuteTime": {
"end_time": "2021-03-25T03:10:39.678453Z",
"start_time": "2021-03-25T03:10:36.763061Z"
}
},
"outputs": [
{
"data": {
"text/plain": "'2.3.0'"
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import brainpy as bp\n",
"import brainpy.math as bm\n",
"\n",
"bm.enable_x64() # It's better to enable x64 when performing analysis\n",
"bm.set_platform('cpu')\n",
"\n",
"bp.__version__"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## A simple case"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we test BrainPy with a simple case:\n",
"\n",
"$$\n",
"\\frac{dx}{dt} = \\mathrm{sin}(x) + I,\n",
"$$\n",
"\n",
"where $x \\in [-10, 10]$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As known to us all, this function has multiple fixed points ($\\frac{dx}{dt} = 0$) when $I=0$."
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": "",
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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"xs = np.arange(-10, 10, 0.01)\n",
"\n",
"plt.plot(xs, np.sin(xs))\n",
"plt.scatter([-3*np.pi, -1*np.pi, 1*np.pi, 3 * np.pi], np.zeros(4), s=80, edgecolors='y')\n",
"plt.scatter([-2*np.pi, 0, 2*np.pi], np.zeros(3), s=80, facecolors='none', edgecolors='r')\n",
"plt.axhline(0)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"According to the dynamical theory, at the red hollow points, they are unstable; and for the solid ones, they are stable points. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's come back to BrainPy, and test whether BrainPy can give us the right answer. \n",
"\n",
"As the analysis interfaces in BrainPy only receives [ODEIntegrator](../apis/integrators/generated/brainpy.integrators.ODEIntegrator.rst) or instance of [DynamicalSystem](../apis/auto/simulation/generated/brainpy.simulation.brainobjects.DynamicalSystem.rst), we first define an integrator with BrainPy (if you want to know how to define an ODE integrator, please refer to the tutorial of [Numerical Solvers for ODEs](../tutorial_intg/ode_numerical_solvers.ipynb)):"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"@bp.odeint\n",
"def int_x(x, t, Iext):\n",
" return bp.math.sin(x) + Iext"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is a one-dimensional dynamical system. So we are trying to use [brainpy.analysis.PhasePlane1D](../apis/auto/analysis/generated/brainpy.analysis.lowdim.PhasePlane1D.rst) for phase plane analysis. The usage of phase plane analysis will be detailed in the following section. Now, we just focus on the following four arguments:\n",
"\n",
"- **model**: It specifies the target system to analyze. It can be a list/tuple of [ODEIntegrator](../apis/integrators/generated/brainpy.integrators.ODEIntegrator.rst). However, it can also be an instance of [DynamicalSystem](../apis/auto/simulation/generated/brainpy.simulation.brainobjects.DynamicalSystem.rst). For ``DynamicalSystem`` argument, we will use ``model.ints().subset(bp.ode.ODEIntegrator)`` to retrieve all instances of ODEIntegrator later. \n",
"- **target_vars**: It specifies the variables to analyze. It must be a dict with the format of ````, where ``var_name`` is the variable name, and ``var_interval`` is the boundary of this variable. \n",
"- **pars_update**: Parameters to update. \n",
"- **resolutions**: The resolution to evaluate the fixed points. \n",
"\n",
"Let's try it."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"I am creating the vector field ...\n",
"I am searching fixed points ...\n",
"Fixed point #1 at x=-9.424777960769386 is a stable point.\n",
"Fixed point #2 at x=-6.283185307179586 is a unstable point.\n",
"Fixed point #3 at x=-3.1415926535897984 is a stable point.\n",
"Fixed point #4 at x=3.552755127361717e-18 is a unstable point.\n",
"Fixed point #5 at x=3.1415926535897984 is a stable point.\n",
"Fixed point #6 at x=6.283185307179586 is a unstable point.\n",
"Fixed point #7 at x=9.424777960769386 is a stable point.\n"
]
},
{
"data": {
"text/plain": "",
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pp = bp.analysis.PhasePlane1D(\n",
" model=int_x,\n",
" target_vars={'x': [-10, 10]},\n",
" pars_update={'Iext': 0.},\n",
" resolutions={'x': 0.01}\n",
")\n",
"pp.plot_vector_field()\n",
"pp.plot_fixed_point(show=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Yeah, absolutelty, ``brainpy.analysis.PhasePlane1D`` gives us the right fixed points, and correctly evaluates the stability of these fixed points."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Phase plane is important, because it gives us the intuitive understanding how the system evolves with the given parameters. However, in most cases where we care about how the parameters affect the system behaviors, we should make bifurcation analysis. [brainpy.analysis.Bifurcation1D](../apis/auto/analysis/generated/brainpy.analysis.lowdim.Bifurcation1D.rst) is a convenient interface to help you get the insights of how the dynamics of a 1D system changes with parameters.\n",
"\n",
"Similar to ``brainpy.analysis.PhasePlane1D``, ``brainpy.analysis.Bifurcation1D`` receives arguments like \"model\", \"target_vars\", \"pars_update\", and \"resolutions\". Besides, one more important argument **\"target_pars\"** should be provided, which specifies the range of the target parameter in bifurcation analysis."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here, we systematically change the parameter \"Iext\" from 0 to 1.5. According to the bifurcation theory, we know this simple system has a fold bifurcation when $I=1.0$. Because at $I=1.0$, two fixed points collide with each other into a saddle point and then disappear. Does BrainPy's analysis toolkit ``brainpy.analysis.Bifurcation1D`` is capable of performing these analyses? Let's make a try."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"I am making bifurcation analysis ...\n"
]
},
{
"data": {
"text/plain": "",
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"bif = bp.analysis.Bifurcation1D(\n",
" model=int_x,\n",
" target_vars={'x': [-10, 10]},\n",
" target_pars={'Iext': [0., 1.5]},\n",
" resolutions={'Iext': 0.005, 'x': 0.05}\n",
")\n",
"bif.plot_bifurcation(show=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Once again, BrainPy analysis toolkit gives the right answer. It tells us how does the fixed points evolve when the parameter $I$ is increasing. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is worthy to note that bifurcation analysis in BrainPy is hard to find out the saddle point (when $I=0$ for this system). This is because the saddle point at the bifurcation just exists at a moment. While the numerical method used in BrainPy analysis toolkit is almost impossible to evaluate the point exactly at the saddle. However, if the user has the minimal knowledge about the bifurcation theory, saddle point (the collision point of two fixed points) can be easily inferred from the fixed point evolution."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"BrainPy's analysis toolkit is highly useful, especially when the mathematical equations are too complex to get analytical solutions. The example please refer to the tutorial [Anlysis of A Decision Making Model](./decision_making_model.ipynb). "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Phase plane analysis"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Phase plane analysis is one of the most important techniques for studying the behavior of nonlinear systems, since there is usually no analytical solution for a nonlinear system. BrainPy can help users to plot phase plane of 1D systems or 2D systems. Specifically, we provide [brainpy.analysis.PhasePlane1D](../apis/auto/analysis/generated/brainpy.analysis.lowdim.PhasePlane1D.rst) and [brainpy.analysis.PhasePlane2D](../apis/auto/analysis/generated/brainpy.analysis.lowdim.PhasePlane2D.rst). It can help to plot:\n",
"\n",
"- **Nullcline**: The zero-growth isoclines, such as $g(x, y)=0$ and $g(x, y)=0$.\n",
"- **Fixed points**: The equilibrium points of the system, which are located at all the nullclines intersect.\n",
"- **Vector field**: The vector field of the system.\n",
"- **Limit cycles**: The limit cycles.\n",
"- **Trajectories**: A simulation trajectory with the given initial values."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We have talked about ``brainpy.analysis.PhasePlane1D`` in above. Now we focus on ``brainpy.analysis.PhasePlane2D`` by using a well-known neuron model FitzHugh-Nagumo model. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The FitzHugh-Nagumo model is given by:\n",
"\n",
"$$ \n",
"\\frac {dV} {dt} = V(1 - \\frac {V^2} 3) - w + I_{ext} \\\\\n",
"\\tau \\frac {dw} {dt} = V + a - b w \n",
"$$\n",
"\n",
"There are two variables $V$ and $w$, so this is a two-dimensional system with three parameters $a, b$ and $\\tau$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the system to analyze, users can define it by using the pure ``brainpy.odeint`` or define it as a class of ``DynamicalSystem``. For this FitzHugh-Nagumo model, we define it as a class because later we will perform simulation to verify the analysis results. "
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"class FitzHughNagumoModel(bp.DynamicalSystem):\n",
" def __init__(self, method='exp_auto'):\n",
" super(FitzHughNagumoModel, self).__init__()\n",
"\n",
" # parameters\n",
" self.a = 0.7\n",
" self.b = 0.8\n",
" self.tau = 12.5\n",
"\n",
" # variables\n",
" self.V = bm.Variable(bm.zeros(1))\n",
" self.w = bm.Variable(bm.zeros(1))\n",
" self.Iext = bm.Variable(bm.zeros(1))\n",
"\n",
" # functions\n",
" def dV(V, t, w, Iext=0.): \n",
" return V - V * V * V / 3 - w + Iext\n",
" def dw(w, t, V, a=0.7, b=0.8): \n",
" return (V + a - b * w) / self.tau\n",
" self.int_V = bp.odeint(dV, method=method)\n",
" self.int_w = bp.odeint(dw, method=method)\n",
"\n",
" def update(self, tdi):\n",
" self.V.value = self.int_V(self.V, tdi.t, self.w, self.Iext, tdi.dt)\n",
" self.w.value = self.int_w(self.w, tdi.t, self.V, self.a, self.b, tdi.dt)\n",
" self.Iext[:] = 0."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"model = FitzHughNagumoModel()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we perform a phase plane analysis with parameters $a=0.7, b=0.8, \\tau=12.5$, and input $I_{ext} = 0.8$."
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"pp = bp.analysis.PhasePlane2D(\n",
" model,\n",
" target_vars={'V': [-3, 3], 'w': [-3., 3.]},\n",
" pars_update={'Iext': 0.8}, \n",
" resolutions={'V': 0.01, 'w': 0.01},\n",
")"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"ExecuteTime": {
"end_time": "2021-03-24T11:58:24.172655Z",
"start_time": "2021-03-24T11:58:18.870967Z"
},
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"I am computing fx-nullcline ...\n",
"I am evaluating fx-nullcline by optimization ...\n",
"I am computing fy-nullcline ...\n",
"I am evaluating fy-nullcline by optimization ...\n",
"I am creating the vector field ...\n",
"I am searching fixed points ...\n",
"I am trying to find fixed points by optimization ...\n",
"\tThere are 866 candidates\n",
"I am trying to filter out duplicate fixed points ...\n",
"\tFound 1 fixed points.\n",
"\t#1 V=-0.2729223248464073, w=0.5338542697673022 is a unstable node.\n",
"I am plotting the trajectory ...\n"
]
},
{
"data": {
"text/plain": "",
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# By defaut, nullclines will be plotted as points, \n",
"# while we can set the plot style as the line\n",
"pp.plot_nullcline(x_style={'fmt': '-'}, y_style={'fmt': '-'})\n",
"\n",
"# Vector field can plotted as two ways:\n",
"# - plot_method=\"streamplot\" (default)\n",
"# - plot_method=\"quiver\"\n",
"pp.plot_vector_field()\n",
"\n",
"# There are many ways to search fixed points. \n",
"# By default, it will use the nullcline points of the first \n",
"# variable (\"V\") as the initial points to perform fixed point searching\n",
"pp.plot_fixed_point()\n",
"\n",
"# Trajectory plotting receives the setting of the initial points.\n",
"# There may be multiple trajectories, therefore the initial points \n",
"# should be provived as a list/tuple/numpy.ndarray/Array\n",
"pp.plot_trajectory({'V': [-2.8], 'w': [-1.8]}, duration=100.)\n",
"\n",
"# show the phase plane figure\n",
"pp.show_figure()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see an unstable-node at the point ($V=-0.27, w=0.53$) inside a limit cycle. \n",
"\n",
"We can run a simulation with the same parameters and initial values to verify the periodic activity that correspond to the limit cycle."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"ExecuteTime": {
"end_time": "2021-03-24T11:58:24.378721Z",
"start_time": "2021-03-24T11:58:24.172655Z"
},
"scrolled": false
},
"outputs": [
{
"data": {
"text/plain": " 0%| | 0/1000 [00:00",
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"runner = bp.DSRunner(model, monitors=['V', 'w'], inputs=['Iext', 0.8])\n",
"runner.run(100.)\n",
"\n",
"bp.visualize.line_plot(runner.mon.ts, runner.mon.V, legend='V')\n",
"bp.visualize.line_plot(runner.mon.ts, runner.mon.w, legend='w', show=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Understanding settings"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There are several key settings needed to understand. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ``resolutions``"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"``resolutions`` is one of the most important parameters in PhasePlane and Bifurcation analysis toolkits of BrainPy. It is very important because it has a profound impact on the efficiency of model analysis. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can set ``resolutions`` with the following ways.\n",
"\n",
"1. **None**. If we detect there is no resolution setting for any variable, the corresponding resolution for this variable will be $\\frac{\\mathrm{max\\_value} - \\mathrm{min\\_value}}{20}$.\n",
"2. **A float**. It sets a same resolution for each target variable and parameter. \n",
"3. **A dict**. Specify different resolutions for individual variable/parameter. It can be a *float*, or a vector with the format of *Array* or *numpy.ndarray*. \n",
"\n",
"```{Note}\n",
"It is highly recommended that users specify the resolution to specific parameters or variables by a dict rather than set a float value, which will be applied to all variables. Otherwise, the computation will occupy too much memory if the resolution is set very small. For example, if you want to set the resolution of variable `x` as 0.01, please use `resolutions={'x': 0.01}`.\n",
"```\n",
"\n",
"Enabling set ``resolutions`` with a tensor will give the user the maximal flexibility. Usually, the numerical analysis does not work well at inflection points. Therefore, we can increase the granularity near the inflection points. For example, if there is an inflection point at $1$, we can set the resolution with:"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"r1 = bm.arange(0.00, 0.95, 0.01)\n",
"r2 = bm.arange(0.95, 1.01, 0.001)\n",
"r3 = bm.arange(1.05, 1.50, 0.01)\n",
"resolution = bm.concatenate([r1, r2, r3])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Tips**: For bifurcation analysis, usually we need set a small resolution for parameters, leaving the resolutions of variables as the default. Please see in the following examples."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ``vars`` and ``pars``"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What can be set as variables ``*_vars`` or parameters ``*_pars`` (such as ``target_vars`` or ``target_pars``) for further analysis? Actually, the variables and parameters are recognized as the same with the programming paradigm of [ODE numerical integrators](../tutorial_intg/ode_numerical_solvers.ipynb). Simply speaking, the arguments before ``t`` will be defined as variables, while arguments after ``t`` will be parameters. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"BrainPy's analysis toolkit only support one variable in one differential equation. It cannot analyze the joint differential equation in which multiple variables are defined in the same function. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Moreover, the low-dimensional analyzers in BrainPy cannot analyze dynamical system depends on time $t$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Bifurcation analysis"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Nonlinear dynamical systems are characterized by its parameters. When the parameter changes, the system's behavior will change qualitatively. Therefore, we take care of how the system changes with the smooth change of parameters. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Codimension 1 bifurcation analysis**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We will first see the codimension 1 bifurcation analysis of the model. For example, we vary the input $I_{ext}$ between 0 and 1 and see how the system change its stability."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"ExecuteTime": {
"end_time": "2021-03-24T11:58:26.557712Z",
"start_time": "2021-03-24T11:58:24.381727Z"
},
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"I am making bifurcation analysis ...\n",
"I am filtering out fixed point candidates with auxiliary function ...\n",
"I am trying to find fixed points by optimization ...\n",
"\tThere are 5000 candidates\n",
"I am trying to filter out duplicate fixed points ...\n",
"\tFound 500 fixed points.\n"
]
},
{
"data": {
"text/plain": "",
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jrR63LYHfBBaR7iF73ECyRvStDwHLipA1oi/Z41o/q21Nd1kO+qSTTuLJJ59k7969lJeXs3DhQk488URmzJjBE088QVlZGUD9EFBOTk79J4I99dRTVFVVAbB582aGDh3KlVdeyfe+9z1WrVrV5u+jNVoOWkSSwiLG4O/lUbF+J1Xbyoke3pvscQOxyIFnuInqLstBT5w4kUsvvbR+iecrrriCCRMmADBnzhymTZtGRkYGEyZMYN68eVx55ZWcffbZTJ48mRkzZtQPHb388svcddddRKNR+vTpc9BXAFoOWkRapOWg04+WgxYRkTYpAEREQkoBICKtSqdh4rBr799KASAiLcrOzqasrEwhkAbcnbKyMrKzsxP+Gc0CEpEWDR8+nJKSErQQY3rIzs5m+PDhCW+vABCRFkWjUUaNGhV0GdJJNAQkIhJSCgARkZBSAIiIhJQCQEQkpBQAIiIhpQAQEQkpBYCISEgpAEREQkoBICISUgoAEZGQUgCIiISUAkBEJKQUACIiIaUAEBEJKQWAiEhIKQBEREIq0AAws9+Y2XYzWx1kHSIiYRT0FcA84LSAaxARCaVAA8DdlwI7g6xBRCSsgr4CEBGRgHT5ADCzWWa2wsxW7NixI+hyRES6jS4fAO7+kLsXunvhkCFDgi5HRKTb6PIBICIinSPoaaDzgTeAcWZWYmbfC7IeEZEwyQzy4O5+UZDHFxEJMw0BiYiElAJARCSkFAAiIiGlABARCSkFgIhISCkARERCSgEgIhJSCgARkZBSAIiIhJQCQEQkpBQAIiIhpQAQEQmpQBeDExGRDojVwLrnYdkDsO+fMO4MmPYfkJnVrt0oAERE0kF1Jfz9Tlj3DJRtBK/64rXta2D5/4Pr329XCCgARES6oroO/71nYe/nUL6t9e0rPoOld8HX5iR8CAWAiEhXUdfpr/1vKFvf/p//6K12ba4AEBEJSqwG1v8VVv8JPl4NOzvQ6Tc0Ykq7NlcAiIikWqwG1j4LT/8bVO5Kzj6zB8BJN7TrRxQAIiKp0NpN3INhEfjKdTD9Js0CEhHpMuqma77xayh5I3n7jWTB4C/BuDM7NP2zjgJARCTZqivh5V/AG/dDTUVy9tl/BAw4Eo6fDeNOh0jGQe9SASAikgzJPttP0ll+axQAIiIHo7oSltwOr9938OP6GT1geCEcf3XSzvJbowAQEWmvpJ7tG4w8AU74t5R0+g0pAEREElU3ffOpq6Fqd8f3k4LhnUQoAERE2pKsYZ4e/eCsX8Mx30jpmX5LAg0AMzsN+BWQATzs7ncEWY+ISL1kDfNk9oyv1pl3How9tUt0/HVaDAAz+zXwe3d/vTMObGYZwH3AKUAJsNzMnnb3tZ1xPBGRhCRlmCe4cf32aO0K4H3g/5jZYcACYL67FyXx2JOBD9z9QwAz+wNwNqAAEJHUS8YwT0aP+AyeDrwrNwgtBoC7/wr4lZkdCVwIPGpm2cB84A/uvuEgj30E8FGDxyXAASsZmdksYBbAyJEjD/KQIiINJGWYJz3O9pvT5j0Ad98M3AncaWYTgN8APyU+bn8wrLnDNXP8h4CHAAoLCw94XUSk3ZIxzHMQa/B0FW0GgJlFgdOIXwXMAP4O3JqEY5cAIxo8Hg608YkHIiIdVLf08rt/hPXPdXyJhjQb5mlNazeBTwEuAs4ElgF/AGa5e3mSjr0cGGNmo4CtxAPm20nat4hIXFKWXk7fYZ7WtHYFcBPwe+B6d9+Z7AO7e7WZXQP8lfhw0m/cfU2yjyMiIZSss/1uMMzTmtZuAk/v7IO7+3PAc519HBEJgbobum/eB1tXQKyy4/vqRsM8rdE7gUUkfTXs9EuWH+RibN1zmKc1CgARSS/JGt6p082HeVqjABCRrq9hp7/heajed/D7jPaKf7jKtB+HruOvowAQka6nrsNf/Sf4ZA3888ODG9OvF75hntYoAESka+iMs/w6OttvlgJARILRaWf5tbrwKpxdhQJARFKjbsbOW/fDzk2wdzvEDvIjFJsacjQMy4Xcb6nTT4ACQEQ6R9MOv3z7wX9mbnM0vNNhCgAROXgNO/t/bo4/Lt8O1HTO8VL84endlQJARNqvuhJe/kX8hm1FOVTu7pyz+zqRLBh0FAw7VsM7SaQAEJGWNbxR++la2L+79uz+484/ts7yO50CQETiqivh73fCe89CxW7wGOzdkfwbtS3RWX7KKQBEwqhhZ79vF1Tthf3/TG0NfY+Id/ADRsZv4uosP+UUACLdVdN59ntLwR0yslIzhNNUv+GQ3T8+N3/af2jGThegABBJdw1XxCzdEO/kM3vEO/xkvrGqPfocHh86ivaE/PM1RbOLUgCIpIPmbsbi8c6+fEfnzsBpUwT6Ha6z+zSkABDpImLVMXYt3szeNaX4/hrcwQzcHSsvxWoqyLTj6JOxlZ4Z6zGLpb5Ii0KfoRq77yYUACIp1GInXxODPQe+acpr/+v0x+lPpQ9jZ3UeWTXFDMn6n50XAnUdPQaRiDr7bkoBIJJEseoYny/axN63d+CV1Vg0AyeRTr41dsAzlf5lKmLH0TNjeRKqzoSe/eMfjDJkrObdh4gCQCRBHnP2rSuj/J3tVH28h1h5NbjXd/J4DHY37uB9X/wMve1Ovr0yqfLR9KQdAWAZ0GMARLM1hCOAAkAEaNy5V39STk1FDeBQXXujNTMC5dXQzIhLXSefWtVE7cPmX8oeGJ99YxHo0ReGfVlvrJJmKQCk2zuYzv0LQXTyTX1xHZEV3Uh2/0/AhsfHl7L7aQaOtJsCQNKWx5y9a0rZ89pWqnZW1M6Yof47OFTFoCLWxhhMV+jcm9Ev2qhNZhEyD+lBn6lH0PPLJ2KRK4OuUNKcAkC6nKYde8Oz9frxdhx2Vzfq2L3J97TQoJOPRIxIdibZXx5Ev6+NJJIZCbo66eYUAJIyLc9zh/pOPhaD/d5iLx7MeHvHWb/oF7OA1MlLFxNIAJjZ+cAtwDHAZHdfEUQdcnBiMWdzcSnrV3xC2Ud72LenEtzJyMoEHMPwBt9P5ot/cHUTG9PqbL0pA7IjjaZ6Nh6mGYRFDpzCKdJVBHUFsBo4F/jPgI4vLaiujrHi2X+wsWg7VftqGnXgONRUx8CdSDSDij1VeHMf+LT3wPVnxvWIkJkdwSxNOkQD+mRCzRdDT5iRkZ1B9NA+9Bw/hJ5HD1QHL2ktkABw93VA+nQGaSoWczYV7eDtlz5id+leaKYjb3i2XhOroWJXoh/h176hmEGZXehvrc5dBNA9gLTRcLhlZ0k5+yuqWuzIHY9PfWxyk7RZzZytd4ayamdwZ4dABOgTPeC+ggEZfbKIHqbOXaShTgsAM1sEHNrMS3Pc/al27GcWMAtg5MiRSaouWHVn5qsWb+HzT8rxZjrwhIdb6qSoI++o9ftjjO4RIdowkcyaWeSgGX0bn63XjbeDztpFDkanBYC7fz1J+3kIeAigsLCwS90zbG9HnpGViXuMit3VeNMRlFY78PSa+dKS53dVM65HhEOjRtSM3occeLaOO5GsTCI9NVNGpLOFfggo0ZksSenIu/hZ+kEzyOoVITOaicXP06HBd7MIpb0y6ZM/mMIzR5Gpjl0kUEFNAz0H+L/AEOBZMyty91M7ur+OnIlT+9y+dsxkSei1bqbXgChW24G7x+fyO05GNJOIQVZ2JoOG9+FLhcPIyRtMREMwImkjqFlAC4GFydhXLOY8+ctVfPz+541fUAd+gF4DsuJx2KQjtyZn6T16ZZKjs3SRbi/th4C2rC7j0427gi4j9SLQs28Ub6EjdwevcTJ7ZDBm0jAmfWO0OnMRaSTtA2DHR7uJxbrUveF2y+oVITPrwA5cwy0i0pnSPgCGjOhLJGJdIgQS6chNwywi0kWkfQCMzB3EsKP6HXgPoKNamMmijlxEupu0D4BIxPjm/5gYX/Jg8RY++6S8xTHx5m58moZWRCSk0j4AIB4CoycOZfTEoUGXIiKSNjRmISISUgoAEZGQUgCIiISUAkBEJKQUACIiIaUAEBEJKQWAiEhIKQBEREJKASAiElIKABGRkFIAiIiElAJARCSkFAAiIiGlABARCSkFgIhISCkARERCSgEgIhJSCgARkZBSAIiIhJQCQEQkpAIJADO7y8zeM7NiM1toZgOCqENEJMyCugL4G5Dr7vnABuAnAdUhIhJagQSAu7/o7tW1D98EhgdRh4hImHWFewCXA8+39KKZzTKzFWa2YseOHSksS0Ske8vsrB2b2SLg0GZemuPuT9VuMweoBh5vaT/u/hDwEEBhYaF3QqkiIqHUaQHg7l9v7XUzuwT4BjDD3dWxi4ikWKcFQGvM7DTgRmCau+8NogYRkbAL6h7Ar4G+wN/MrMjMHgyoDhGR0ArkCsDdvxTEcUVE5AtdYRaQiIgEQAEgIhJSCgARkZBSAIiIhJQCQEQkpBQAIiIhpQAQEQkpBYCISEgpAEREQkoBICISUgoAEZGQUgCIiISUAkBEJKQUACIiIaUAEBEJKQWAiEhIKQBEREJKASAiElIKABGRkFIAiIiElAJARCSkFAAiIiGlABARCSkFgIhISCkARERCKpAAMLOfm1mxmRWZ2YtmdngQdYiIhFlQVwB3uXu+uxcAzwA3B1SHiEhoBRIA7r6rwcPegAdRh4hImGUGdWAzux34LvA5MD2oOkREwqrTrgDMbJGZrW7m62wAd5/j7iOAx4FrWtnPLDNbYWYrduzY0VnlioiEjrkHO/piZkcCz7p7blvbFhYW+ooVK1JQlYhI92FmK929sOnzQc0CGtPg4VnAe0HUISISZkHdA7jDzMYBMWAzcFVAdYiIhFYgAeDu3wriuCIi8oXA7wG0h5ntIH7F0JLBQGmKyumKwtz+MLcd1H61v/X2H+nuQ5o+mVYB0BYzW9HcjY6wCHP7w9x2UPvV/o61X2sBiYiElAJARCSkulsAPBR0AQELc/vD3HZQ+9X+DuhW9wBERCRx3e0KQEREEqQAEBEJqbQMADM7zczWm9kHZvbjZl43M7u39vViM5sYRJ2dIYG2f6e2zcVm9rqZjQ+izs7SVvsbbDfJzGrM7LxU1tfZEmm/mZ1c+2FLa8zs76musTMl8O+/v5n9t5m9U9v+y4KoszOY2W/MbLuZrW7h9fb3e+6eVl9ABrARGA1kAe8AX26yzRnA84ABxwNvBV13Ctv+FeCQ2v8/vbu0PdH2N9juJeA54Lyg607x338AsBYYWft4aNB1p7j9NwF31v7/EGAnkBV07Ulq/0nARGB1C6+3u99LxyuAycAH7v6hu1cCfwDObrLN2cBjHvcmMMDMDkt1oZ2gzba7++vu/s/ah28Cw1NcY2dK5G8PcC3wZ2B7KotLgUTa/23gL+6+BcDdu9PvIJH2O9DXzAzoQzwAqlNbZudw96XE29OSdvd76RgARwAfNXhcUvtce7dJR+1t1/eInxF0F22238yOAM4BHkxhXamSyN9/LHCImb1sZivN7Lspq67zJdL+XwPHANuAd4Hr3D2WmvIC1+5+L7BPBDsI1sxzTeeyJrJNOkq4XWY2nXgAfLVTK0qtRNo/F7jR3WviJ4HdSiLtzwSOA2YAPYE3zOxNd9/Q2cWlQCLtPxUoAr4GHAX8zcxe8cYfQ9tdtbvfS8cAKAFGNHg8nHjat3ebdJRQu8wsH3gYON3dy1JUWyok0v5C4A+1nf9g4Awzq3b3J1NSYedK9N9+qbuXA+VmthQYD3SHAEik/ZcBd3h8UPwDM/sHcDSwLDUlBqrd/V46DgEtB8aY2SgzywIuBJ5uss3TwHdr74ofD3zu7h+nutBO0GbbzWwk8Bfg4m5y1tdQm+1391HunuPuOcCfgKu7SecPif3bfwo40cwyzawXMAVYl+I6O0si7d9C/OoHMxsGjAM+TGmVwWl3v5d2VwDuXm1m1wB/JT4r4DfuvsbMrqp9/UHisz/OAD4A9hI/K0h7Cbb9ZmAQcH/tWXC1d5NVEhNsf7eVSPvdfZ2ZvQAUE//ApYfdvdlpg+kmwb//z4F5ZvYu8SGRG929WywTbWbzgZOBwWZWAvwUiELH+z0tBSEiElLpOAQkIiJJoAAQEQkpBYCISEgpAEREQkoBICISUgoAkQSY2Z4O/lyBmZ2R7HpEkkEBINK5CojPzRbpchQAIu1kZjeY2fLaNddvrX3uHDNbVPsuzMPMbEPtu7J/BlxQuz7/BcFWLtJY2r0TWCRIZvYvwBjiSxMb8LSZneTuC83sW8C/AacBP3X3LWZ2M1Do7tcEV7VI8xQAIu3zL7Vfb9c+7kM8EJYS/xyC1cCb7j4/mPJEEqcAEGkfA37h7v/ZzGtHEF9/Z5iZRUK0Dr2kKd0DEGmfvwKXm1kfiH8AjZkNNbNM4FHin8i1Dvj32u13A30DqVSkDVoMTiQBZrbH3es6/euAK2pf2gPMBL4DDHD3fzezvsSXLj4H+JR4aESJXzksSHnxIi1QAIiIhJSGgEREQkoBICISUgoAEZGQUgCIiISUAkBEJKQUACIiIaUAEBEJqf8P7yyPcqLwIegAAAAASUVORK5CYII=\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"analyzer = bp.analysis.Bifurcation2D(\n",
" model,\n",
" target_vars={'V': [-3, 3], 'w': [-3., 3.]},\n",
" target_pars={'Iext': [0., 1.]},\n",
" resolutions={'Iext': 0.002},\n",
")\n",
"\n",
"# \"num_rank\" specifies the number of initial poinits for\n",
"# fixed point optimization under a set of parameters\n",
"analyzer.plot_bifurcation(num_rank=10)\n",
"\n",
"# show figure\n",
"analyzer.show_figure()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Codimension 2 bifurcation analysis**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We simulaneously change $I_{ext}$ and parameter $a$."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"I am making bifurcation analysis ...\n",
"I am filtering out fixed point candidates with auxiliary function ...\n",
"I am trying to find fixed points by optimization ...\n",
"\tThere are 50000 candidates\n",
"I am trying to filter out duplicate fixed points ...\n",
"\tFound 4997 fixed points.\n"
]
},
{
"data": {
"text/plain": "",
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"analyzer = bp.analysis.Bifurcation2D(\n",
" model,\n",
" target_vars=dict(V=[-3, 3], w=[-3., 3.]),\n",
" target_pars=dict(a=[0.5, 1.], Iext=[0., 1.]),\n",
" resolutions={'a': 0.01, 'Iext': 0.01},\n",
")\n",
"analyzer.plot_bifurcation(num_rank=10, tol_aux=1e-9)\n",
"analyzer.show_figure()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fast-slow system bifurcation"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"BrainPy also provides a tool for fast-slow system bifurcation analysis by using [brainpy.analysis.FastSlow1D](../apis/auto/analysis/generated/brainpy.analysis.lowdim.FastSlow1D.rst) and [brainpy.analysis.FastSlow2D](../apis/auto/analysis/generated/brainpy.analysis.lowdim.FastSlow2D.rst). This method is proposed by John Rinzel [1, 2, 3]. (J Rinzel, 1985, 1986, 1987) proposed that in a fast-slow dynamical system, we can treat the slow variables as the bifurcation parameters, and then study how the different value of slow variables affect the bifurcation of the fast sub-system.\n",
"\n",
"\n",
"Fast-slow bifurcation methods are very useful in the bursting neuron analysis. I will illustrate this by using the Hindmarsh-Rose model. The Hindmarshâ€“Rose model of neuronal activity is aimed to study the spiking-bursting behavior of the membrane potential observed in experiments made with a single neuron. Its dynamics are governed by:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\frac{d V}{d t} &= y - a V^3 + b V^2 - z + I\\\\\n",
"\\frac{d y}{d t} &= c - d V^2 - y\\\\\n",
"\\frac{d z}{d t} &= r (s (V - V_{rest}) - z)\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, let's define the Hindmarshâ€“Rose model with BrainPy."
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"ExecuteTime": {
"end_time": "2021-03-24T11:58:29.650571Z",
"start_time": "2021-03-24T11:58:29.637572Z"
}
},
"outputs": [],
"source": [
"a = 1.\n",
"b = 3.\n",
"c = 1.\n",
"d = 5.\n",
"s = 4.\n",
"x_r = -1.6\n",
"r = 0.001\n",
"Vth = 1.9\n",
"\n",
"\n",
"@bp.odeint\n",
"def int_x(x, t, y, z, Isyn):\n",
" return y - a * x ** 3 + b * x * x - z + Isyn\n",
"\n",
"@bp.odeint\n",
"def int_y(y, t, x):\n",
" return c - d * x * x - y\n",
"\n",
"@bp.odeint\n",
"def int_z(z, t, x):\n",
" return r * (s * (x - x_r) - z)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now can start to analysis the underlying bifurcation mechanism."
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"I am making bifurcation analysis ...\n",
"I am filtering out fixed point candidates with auxiliary function ...\n",
"I am trying to find fixed points by optimization ...\n",
"\tThere are 20000 candidates\n",
"I am trying to filter out duplicate fixed points ...\n",
"\tFound 1156 fixed points.\n"
]
},
{
"data": {
"text/plain": "",
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"analyzer = bp.analysis.FastSlow2D(\n",
" [int_x, int_y, int_z],\n",
" fast_vars={'x': [-3, 3], 'y': [-10., 5.]},\n",
" slow_vars={'z': [-5., 5.]},\n",
" pars_update={'Isyn': 0.5},\n",
" resolutions={'z': 0.01}\n",
")\n",
"analyzer.plot_bifurcation(num_rank=20)\n",
"analyzer.show_figure()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## References\n",
"\n",
"[1] Rinzel, John. \"Bursting oscillations in an excitable membrane model.\" In Ordinary and partial differential equations, pp. 304-316. Springer, Berlin, Heidelberg, 1985.\n",
" \n",
"[2] Rinzel, John , and Y. S. Lee . On Different Mechanisms for Membrane Potential Bursting. Nonlinear Oscillations in Biology and Chemistry. Springer Berlin Heidelberg, 1986.\n",
"\n",
"[3] Rinzel, John. \"A formal classification of bursting mechanisms in excitable systems.\" In Mathematical topics in population biology, morphogenesis and neurosciences, pp. 267-281. Springer, Berlin, Heidelberg, 1987.\n"
]
}
],
"metadata": {
"hide_input": false,
"jupytext": {
"encoding": "# -*- coding: utf-8 -*-"
},
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.7"
},
"latex_envs": {
"LaTeX_envs_menu_present": true,
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"autocomplete": true,
"bibliofile": "biblio.bib",
"cite_by": "apalike",
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