Phase Propagations in a Coupled Oscillator--Excitor System of FitzHugh--Nagumo Models

A one-dimensional array of 2N+1 automata with FitzHugh--Nagumo dynamics, in which one is set to be oscillatory and the others are excitable, is investigated with bi-directional interactions. We find that 1:1 rhythm propagation in the array depends on the appropriate couple strength and the excitability of the system. On the two sides of the 1:1 rhythm area in parameter space, two different kinds of dynamical behaviour of the pacemaker, i.e. phase-locking phenomena and canard-like phenomena, are shown. The latter is found in company with chaotic pattern and period doubling bifurcation. When the coupling strength is larger than a critical value, the whole system ends to a steady state.