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The FitzHugh-Nagumo system describes a prototype of an excitable system (e.g., a neuron). | 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. | 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== | ==References== | ||
Revision as of 15:21, 20 November 2012
Description
The FitzHugh-Nagumo system describes a prototype of an excitable system (e.g., a neuron). If the external stimulus exceeds a certain threshold value, the system will exhibit a characteristic excursion in phase space, before the variables and relax back to their rest values. This behaviour is typical for spike generations (=short elevation of membrane voltage ) 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, \\ }
References
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