The Fokker-Planck approach Numerical solutions

In the previous section the stochastic FitzHugh-Nagumo system has been treated using the Langevin eqs. 1.31. Alternatively it can be described by the Fokker-Planck equation (FPE) (cf. subsec. 1.3.3). In the case of the 

FHN system an analytic solution of this equation cannot be given. Here we therefore use a numeric approach. The equation under study reads  

We want to mention that the probability density further off the maxima becomes extremely small for small noise intensities so that numerical errors will eventually dominate the obtained results. In particular we cannot exclude a second maximum for the low noise case in Fig. 1.5. However we have also performed simulations with varying e (separation of the timescales). For high e (small separation) we find states with clearly one maximum only. 

We thus find, depending on the noise intensity and the separation of the timescale three qualitatively different regimes. In these regimes differ- 

We have also performed simnlations witli noise in tlie activator variable. The obtained re.suIts differ only quantitatively from the ones presented for inhibitor noise. 

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