Fitzhugh-Nagumo Model

class pints.toy.FitzhughNagumoModel(y0=None)[source]

Fitzhugh-Nagumo model of the action potential [1].

Has two states, and three phenomenological parameters: a , b, c. All states are visible

\[\frac{d \mathbf{y}}{dt} = \mathbf{f}(\mathbf{y},\mathbf{p},t)\]

where

\[\begin{split}\mathbf{y} &= (V,R)\\ \mathbf{p} &= (a,b,c)\end{split}\]

The RHS, jacobian and change in RHS with the parameters are given by

\[\begin{split}\begin{align} \mathbf{f}(\mathbf{y},\mathbf{p},t) &= \left[\begin{matrix} c \left(R - V^{3}/3+V\right) \\ - \frac{1}{c} \left(R b + V - a\right) \end{matrix}\right] \\ \frac{\partial \mathbf{f}}{\partial \mathbf{y}} &= \left[\begin{matrix} c \left(1- V^{2}\right) & c \\ - \frac{1}{c} & - \frac{b}{c} \end{matrix}\right] \\ \frac{\partial \mathbf{f}}{\partial \mathbf{p}} &= \left[\begin{matrix} 0 & 0 & R - V^{3}/3 + V\\ \frac{1}{c} & - \frac{R}{c} & \frac{1}{c^{2}} \left(R b + V - a\right) \end{matrix}\right] \end{align}\end{split}\]

Extends pints.ForwardModelS1, pints.toy.ToyODEModel.

Parameters:y0 – The system’s initial state. If not given, the default [-1, 1] is used.

References

[1]A kinetic model of the conductance changes in nerve membrane Fitzhugh (1965) Journal of Cellular and Comparative Physiology. https://doi.org/10.1002/jcp.1030660518
initial_conditions()

Returns the initial conditions of the model.

jacobian(y, t, p)[source]

See pints.ToyODEModel.jacobian().

n_outputs()[source]

See pints.ForwardModel.n_outputs().

n_parameters()[source]

See pints.ForwardModel.n_parameters().

n_states()

Returns number of states in underlying ODE. Note: will not be same as n_outputs() for models where only a subset of states are observed.

set_initial_conditions(y0)

Sets the initial conditions of the model.

simulate(parameters, times)

See pints.ForwardModel.simulate().

simulateS1(parameters, times)

See pints.ForwardModelS1.simulateS1().

suggested_parameters()[source]

See pints.toy.ToyModel.suggested_parameters().

suggested_times()[source]

See pints.toy.ToyModel.suggested_times().