Akihisa Tamura, Tetsushi Ueta, Shigeki Tsuji, Bifurcation Analysis of Izhikevich Neuron Model, Watam Press, Dynamics of Continuous, Discrete and Impulsive Systems. Series A: Mathematical Analysis, Vol.16, No.6, 849-862, Waterloo, Dec. 2009.
Abstract: An autonomous differential equation with jumps has been proposed by Izhikevich for a demonstration of various spiking waves by changing its parameters. Some well-known firing patterns of this model are shown by numerical simulations, however bifurcation analysis of the model has not been investigated in detail. In this paper, we apply our numerical computation algorithm to this model. Although it is a challenge to manage jumps with the Poincar´e mapping and we obtain bifurcation parameter values by a shooting method. As a result, we conclude that some spiking modes are caused by local bifurcation of limit cycles.