neurodynex3.phase_plane_analysis package¶
Submodules¶
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:
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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]
Returns: (v_fp, w_fp) fixed point of the equations
Return type: tuple
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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]
Returns: (t, v, w) tuple for solutions
Return type: tuple
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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]