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The Fitzhugh-Nagumo model is a model for the excitable dynamics of neural systems. The original, non-spatial version of the model describes a system that, when it is taken away from equilibrium for a sufficient extent by an external stimulus, initially runs away from this equilibrium to follow a extensive route to finally return to the equilibrium.
When set in a 1D spatial setting, it predicts travelling wave dynamics that can explain the transmittance of a signal over a neuron.
When set in a 2D spatial setting, it can predict a wide array of spatial patterns and dynamics, which can be explored in the model above.
The model consists of the following partial differential equations
∂u / ∂t = u - u3 - v + ∇2u
∂v / ∂t = ϵ(u - a1v - ao) + δ∇2v
Here, u is the membrane potential, and v is a recovery variable. ϵ (Epsilon), a0 and a1 are interaction constant, δ stands for the ration between the diffusivity of v to u, and ∇2 is the laplacian operator in two spatial dimensions.
We adopted the version of the spatial Fitzhugh-Nagumo model that is described in “The Nonlinear Physics of Ecosystems” by Ehud Meron (2015).