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 $N=2\mathrm{}$ case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case $N>\mathrm{}2.\mathrm{}$ 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.

• Received 21 November 2002

DOI:https://doi.org/10.1103/PhysRevE.67.066222