Analysis of routes to chaos in Izhikevich neuron model with resetting process

Recently, according to the development of the brain measurement technology, it has been recognized that the information is transmitted among neurons by the spike timing instead of the firing rate of neurons. Therefore, the spiking neuron models which can describe the spike timing have been attracting a lot of attention. Izhikevich neuron model, which combines continuous spike-generation mechanisms and discontinuous resetting process after spikes as a hybrid system, can reproduce major spike patterns observed in the cerebral cortex only by tuning a few parameters of it 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.