Pair of excitable FitzHugh-Nagumo elements: Synchronization, multistability, and chaos

T. Yanagita, T. Ichinomiya, Y. Oyama
2005 Physical Review E  
We analyze a pair of excitable FitzHugh-Nagumo elements, each of which is coupled repulsively. While the rest state for each element is globally stable for a phase-attractive coupling, various firing patterns, including cyclic and chaotic firing patterns, exist in an phase-repulsive coupling region. Although the rest state becomes linearly unstable via a Hopf bifurcation, periodic solutions associated to the firing patterns is not connected to the Hopf bifurcation. This means that the solution
more » ... ranch emanating from the Hopf bifurcation is subcritical and unstable for any coupling strength. Various types of cyclic firing patterns emerge suddenly through saddle-node bifurcations. The parameter region in which different periodic solutions coexist is also found.
doi:10.1103/physreve.72.056218 pmid:16383738 fatcat:sb73wkasinaftaoehcza46jzoy