Chaotic States Induced By Resetting Process In Izhikevich Neuron Model

Sou Nobukawa 1 , Haruhiko Nishimura 2 , Teruya Yamanishi 1  and Jian-Qin Liu 3
  • 1 Department of Management Information Science, Fukui University of Technology, 3-6-1 Gakuen, Fukui, Fukui, 910-8505 Japan
  • 2 Graduate School of Applied Informatics, University of Hyogo, 7-1-28 Chuo-ku, Kobe, Hyogo, 650-8588 Japan
  • 3 Center for Information and Neural Networks, National Institute of Information and Communications Technology, 588-2 Iwaoka, Iwaoka-cho, Nishi-ku, Kobe, Hyogo, 651-2492 Japan


Several hybrid neuron models, which combine continuous spike-generation mechanisms and discontinuous resetting process after spiking, have been proposed as a simple transition scheme for membrane potential between spike and hyperpolarization. As one of the hybrid spiking neuron models, Izhikevich neuron model can reproduce major spike patterns observed in the cerebral cortex only by tuning a few parameters and also exhibit chaotic states in specific conditions. However, there are a few studies concerning the chaotic states over a large range of parameters due to the difficulty of dealing with the state dependent jump on the resetting process in this model. In this study, we examine the dependence of the system behavior on the resetting parameters by using Lyapunov exponent with saltation matrix and Poincaré section methods, and classify the routes to chaos.

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