Master Stability Functions of Networks of Izhikevich Neurons

Abstract

Synchronization has attracted the interest of many areas where the systems under study can be described by complex networks. Among such areas is neuroscience, where is hypothesized that synchronization plays a role in many functions and dysfunctions of the brain. We study the linear stability of synchronized states in networks of Izhikevich neurons using Master Stability Functions, and to accomplish that, we exploit the formalism of saltation matrices. Such a tool allows us to calculate the Lyapunov exponents of the Master Stability Function (MSF) properly since the Izhikevich model displays a discontinuity within its spikes. We consider both electrical and chemical couplings, as well as total and partially synchronized states. The MSFs calculations are compared with a measure of the synchronization error for simulated networks. We give special attention to the case of electric and chemical coupling, where a riddled basin of attraction makes the synchronized solution more sensitive to perturbations.