Proceeding of International Conference
Daisuke Ito, Tetsushi Ueta, Bifurcation Analysis of Two Coupled Izhikevich Oscillators, Proc. NOLTA2010, 627-630, Cracow, Sep. 2010.
Abstract: A simple oscillator of spiking neurons is pro- posed by Izhikevich. By some numerical experiments, all firing patterns which have been observed in the brain are confirmed at the origin of the mathematical model. Al- though, a detailed bifurcation analysis has been given by the author, no investigation on its coupling system has been done. In this paper, we consider two Izhikevich neurons coupled by a gap junction. By choosing an appropriate Poincare section, we can compute bifurcation set for limit cycles. As a result, period-doubling bifurcation and its cas- cade to chaos is observed by changing the coupling coeffi- cient. We show bifurcation diagrams and numerical simu- lation results.