Semi-passivity and synchronization of diffusively coupled neuronal oscillators

E. Steur, I.Y. (Ivan Yu) Tyukin, H. Nijmeijer

Research output: Contribution to journalArticleAcademicpeer-review

103 Citations (Scopus)
5 Downloads (Pure)

Abstract

We discuss synchronization in networks of neuronal oscillators which are interconnected via diffusive coupling, i.e. linearly coupled via gap junctions. In particular, we present sufficient conditions for synchronization in these networks using the theory of semi-passive and passive systems. We show that the conductance based neuronal models of Hodgkin-Huxley, Morris-Lecar, and the popular reduced models of FitzHugh-Nagumo and Hindmarsh-Rose all satisfy a semi-passivity property, i.e. that is the state trajectories of such a model remain oscillatory but bounded provided that the supplied (electrical) energy is bounded. As a result, for a wide range of coupling configurations, networks of these oscillators are guaranteed to possess ultimately bounded solutions. Moreover, we demonstrate that when the coupling is strong enough the oscillators become synchronized. Our theoretical conclusions are confirmed by computer simulations with coupled Hindmarsh-Rose and Morris-Lecar oscillators. Finally we discuss possible "instabilities" in networks of oscillators induced by the diffusive coupling. © 2009 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)2119-2128
JournalPhysica D : Nonlinear Phenomena
Volume238
Issue number21
DOIs
Publication statusPublished - 2009

Fingerprint

Dive into the research topics of 'Semi-passivity and synchronization of diffusively coupled neuronal oscillators'. Together they form a unique fingerprint.

Cite this