FitzHugh-Nagumo System

Description

The FitzHugh-Nagumo system describes a prototype of an excitable system (e.g., a neuron). If the external stimulus $i_{0} (t)$ exceeds a certain threshold value, the system will exhibit a characteristic excursion in phase space, before the variables $v$ and $w$ relax back to their rest values. This behaviour is typical for spike generations (=short elevation of membrane voltage $v$ ) in a neuron after stimulation by an external input current.

Here, we present the setting from [1], where the equations for the dynamical system read

Failed to parse (syntax error): {\displaystyle \epsilon v_t(x,t)=\epsilon^2v_{xx}(x,t)+f(v(x,t))-w(x,t)+g, \\ }

$w_{t} (x, t) = h v (x, t) - γ w (x, t) + g,$

References

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