# neurodynex3.phase_plane_analysis package¶

## neurodynex3.phase_plane_analysis.fitzhugh_nagumo module¶

This file implements functions to simulate and analyze Fitzhugh-Nagumo type differential equations with Brian2.

Relevant book chapters:

neurodynex3.phase_plane_analysis.fitzhugh_nagumo.get_fixed_point(I_ext=0.0, eps=0.1, a=2.0)[source]

Computes the fixed point of the FitzHugh Nagumo model as a function of the input current I.

We solve the 3rd order poylnomial equation: v**3 + V + a - I0 = 0

Parameters: I – Constant input [mV] eps – Inverse time constant of the recovery variable w [1/ms] a – Offset of the w-nullcline [mV] (v_fp, w_fp) fixed point of the equations tuple
neurodynex3.phase_plane_analysis.fitzhugh_nagumo.get_trajectory(v0=0.0, w0=0.0, I_ext=0.0, eps=0.1, a=2.0, tend=500.0)[source]

Solves the following system of FitzHugh Nagumo equations for given initial conditions:

$\begin{split}\frac{dv}{dt} = \frac{1}{1ms} v (1-v^2) - w + I \\ \frac{dw}{dt} = eps (v + 0.5 (a - w))\end{split}$
Parameters: v0 – Intial condition for v [mV] w0 – Intial condition for w [mV] I – Constant input [mV] eps – Inverse time constant of the recovery variable w [1/ms] a – Offset of the w-nullcline [mV] tend – Simulation time [ms] (t, v, w) tuple for solutions tuple
neurodynex3.phase_plane_analysis.fitzhugh_nagumo.plot_flow(I_ext=0.0, eps=0.1, a=2.0)[source]

Plots the phase plane of the Fitzhugh-Nagumo model for given model parameters.

Parameters: I – Constant input [mV] eps – Inverse time constant of the recovery variable w [1/ms] a – Offset of the w-nullcline [mV]