title: Hopf bifurcation and bursting synchronization in an excitable systems with chemical delayed coupling.
abstract: In this paper we consider the Hopf bifurcation and synchronization in the two coupled Hindmarsh-Rose excitable systems with chemical coupling and time-delay. We surveyed the conditions for Hopf bifurcations by means of dynamical bifurcation analysis and numerical simulation. The results show that the coupled excitable systems with no delay have supercritical Hopf bifurcation, while the delayed system undergoes Hopf bifurcations at critical time delays when coupling strength lies in a particular region. We also investigated the effect of the delay on the transition of bursting synchronization in the coupled system. The results are helpful for us to better understand the dynamical properties of excitable systems and the biological mechanism of information encoding and cognitive activity.
authors.affiliation: School of Science, North China University of Technology, Beijing, 100144 China ; Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019 USA.
authors.forename: Lixia
authors.initials: L
authors.lastname: Duan
authors.affiliation: School of Science, North China University of Technology, Beijing, 100144 China.
authors.forename: Denggui
authors.initials: D
authors.lastname: Fan
authors.affiliation: Department of Dynamics and Control, Beihang University, Beijing, 100191 China.
authors.forename: Qishao
authors.initials: Q
authors.lastname: Lu
keywords: Chemical coupling; Delay; Excitability; Hopf bifurcation; Synchronization