Difference between revisions of "FitzHugh-Nagumo System"

Revision as of 17:21, 20 November 2012

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): \epsilon v_t(x,t)=\epsilon^2v_{xx}(x,t)+f(v(x,t))-w(x,t)+g, \\

$w_t(x,t)=hv(x,t)-\gamma w(x,t)+g,$

References

Contact information:

Tobias Breiten

@@ Line 8: / Line 8: @@
 The FitzHugh-Nagumo system describes a prototype of an excitable system (e.g., a neuron).
 If the external stimulus <math>i_0(t)</math> exceeds a certain threshold value, the system will exhibit a characteristic excursion in phase space, before the variables <math>v</math> and <math>w</math> relax back to their rest values. This behaviour is typical for spike generations (=short elevation of membrane voltage  <math>v</math>) 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
+<math>
+\epsilon v_t(x,t)=\epsilon^2v_{xx}(x,t)+f(v(x,t))-w(x,t)+g, \\
+</math>
+<math>
+ w_t(x,t)=hv(x,t)-\gamma w(x,t)+g,
+</math>
 ==References==