Fitzhugh-Nagumo Model¶
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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.
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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.
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set_initial_conditions
(y0)¶ Sets the initial conditions of the model.
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simulate
(parameters, times)¶
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simulateS1
(parameters, times)¶
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