title: Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling.
abstract: Small lattices of N nearest-neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in an N=2 case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case N>2. Bifurcations found include inverse and direct Hopf and fold limit cycle bifurcations. Typical dynamics for different small time lags and coupling intensities could be excitable with a single globally stable equilibrium, asymptotic oscillatory with symmetric limit cycle, bistable with stable equilibrium and a symmetric limit cycle, and again coherent oscillatory but nonsymmetric and phase shifted. For an intermediate range of time lags, inverse sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo oscillators with the same type of coupling.
authors.affiliation: Department of Physics and Mathematics, Faculty of Pharmacy, University of Beograd, Vojvode Stepe 450 Beograd, Yugoslavia. buric@phy.bg.ac.yu
authors.forename: Nikola
authors.initials: N
authors.lastname: Burić
authors.forename: Dragana
authors.initials: D
authors.lastname: Todorović