Chaos synchronization in gap-junction-coupled neurons

Abstract

Depending on temperature the modified Hodgkin-Huxley (MHH) equations exhibit a variety of dynamical behavior including intrinsic chaotic firing. We analyze synchronization in a large ensemble of MHH neurons that are interconnected with gap junctions. By evaluating tangential Lyapunov exponents we clarify whether synchronous state of neurons is chaotic or periodic. Then, we evaluate transversal Lyapunov exponents to elucidate if this synchronous state is stable against infinitesimal perturbations. Our analysis elucidates that with weak gap junctions, stability of synchronization of MHH neurons shows rather complicated change with temperature. We, however, find that with strong gap junctions, synchronous state is stable over the wide range of temperature irrespective of whether synchronous state is chaotic or periodic. It turns out that strong gap junctions realize the robust synchronization mechanism, which well explains synchronization in interneurons in the real nervous system.