title: Synchronized bifurcation and stability in a ring of diffusively coupled neurons with time delay.
abstract: In this study, we consider a ring of diffusively coupled neurons with distributed and discrete delays. We investigate the synchronized stability and synchronized Hopf bifurcation of this system, as well as deriving some criteria by analyzing the associated characteristic transcendental equation and by taking τ and β as the bifurcation parameters, which are parameters that measure the discrete delay and the strength of nearest-neighbor connection, respectively. Our simulations demonstrated that the numerically observed behaviors were in excellent agreement with the theoretically predicted results. In addition, using numerically simulations, we investigated the effects of τ and β, as well as the diffusion on dynamic behavior. Our numerical results showed that the addition diffusion to a stable delay-differential equation (DDE) system may make it unstable and that the diffusion may make the system synchronous, whereas it is asynchronous without the diffusion term.
authors.affiliation: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
authors.forename: Ling
authors.initials: L
authors.lastname: Wang
authors.affiliation: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China. Electronic address: hyzhao1967@126.com.
authors.forename: Hongyong
authors.initials: H
authors.lastname: Zhao
authors.affiliation: Department of Mathematics, Southeast University, Nanjing 210096, China; Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
authors.forename: Jinde
authors.initials: J
authors.lastname: Cao
mesh_terms: D003198:Computer Simulation; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D013997:Time Factors
keywords: Discrete delay; Distributed delay; Hopf bifurcation; Reaction–diffusion; Ring of neurons