Summary
International Symposium on Nonlinear Theory and its Applications
2010
Session Number:C3L-D
Session:
Number:C3L-D3
Bifurcation analysis of two coupled Izhikevich Oscillators
Daisuke Ito, Tetsushi Ueta, Kazuyuki Aihara,
pp.627-630
Publication Date:2010/9/5
Online ISSN:2188-5079
Summary:
A simple oscillator of spiking neurons is proposed 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. Although, 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 Poincar´e section, we can compute bifurcation set for limit cycles. As a result, period-doubling bifurcation and its cascade to chaos is observed by changing the coupling coefficient. We show bifurcation diagrams and numerical simulation results.