A modified hybrid Izhikevich neuron:modeling, synchronization, and experiments

Abstract

The original Izhikevich neuronal model is described by a nonlinear mathematical model with a static reset map. Due to the fact that the reset is applied instantaneously, it is not easy to implement this model with analog circuits. Consequently, this paper presents a modified Izhikevich neuronal model, in which the static and instantaneous reset is replaced by a dynamic reset, which is physically implementable. Furthermore, the resulting system is modeled as a hybrid system with two discrete modes. Additionally, the occurrence of synchronization in a pair of modified Izhikevich neurons is investigated and a comment on the local stability of the synchronous solution is given. Ultimately, the performance of the modified Izhikevich model is experimentally validated using electronic circuits.