Spatiotemporal dynamics of coupled array of Murali-Lakshmanan-Chua circuits

The circuit recently proposed by Murali, Lakshmanan and Chua (MLC) is one o f the simplest nonautonomous nonlinear electronic circuits which show a var iety of dynamical phenomena including various bifurcations, chaos and so on . In this paper we study the spatiotemporal dynamics in one- and two-dimens ional arrays of coupled MLC circuits both in the absence as well as in the presence of external periodic forces. In the absence of any external force, the propagation phenomena of traveling wavefront and its failure have been observed from numerical simulations. We have shown that the propagation of the traveling wavefront is due to the loss of stability of the steady stat es (stationary front) via subcritical bifurcation coupled with the presence of neccessary basin of attraction of the steady states. We also study the effect of weak coupling on the propagation phenomenon in one-dimensional ar ray which results in the blocking of wavefront due to the existence of a st ationary front. Further we have observed the spontaneous formation of hexag onal patterns (with penta-hepta defects) due to Turing instability in the t wo-dimensional array. We show that a transition from hexagonal to rhombic s tructures occur by the influence of an external periodic force. We also sho w the transition from hexagons to rolls and hexagons to breathing (space-ti me periodic oscillations) motion in the presence of external periodic force . We further analyze the spatiotemporal chaotic dynamics of the coupled MLC circuits (in one dimension) under the influence of external periodic forci ng. Here we note that the dynamics is critically dependent on the system si ze. Above a threshold size, a suppression of spatiotemporal chaos occurs, l eading to a space-time regular (periodic) pattern eventhough the single MLC circuit itself shows a chaotic behavior. Below this critical size, however , a synchronization of spatiotemporal chaos is observed.