THE EFFECT OF TIME DELAY ON SPATIOTEMPORAL DYNAMICS IN ONE-DIMENSIONAL DISCRETE EXCITABLE MEDIA

Abstract

We investigate the effect of time delay on spatiotemporal dynamics in one-dimensional discrete excitable media with local delayed-interactions using coupled sine circle-maps. With the help of the stability analysis and numerical calculation of the pattern complexity entropy, we construct the phase diagram in the parameter space time delay and the nonlinear coupling. We find that the time delay affects the existence and stability of various regular states including homogeneously phase-locked and checkerboard states. In particular, the time delay induces the breakup of the homogeneously phase-locked state into spatiotemporal intermittency and the occurrence of multi-stability that depends on the winding number.