Complex dynamics of coupled map lattices under random asynchronous updating

Abstract

The effects of a new type of asynchronous updating on the dynamical behavior of coupled chaotic maps with nearest neighbor as well as global coupling are studied in this paper. In contrast to synchronous updating, the occurrence of the synchronized fixed point window is observed in the parameter space for nearest neighbor interactions as a consequence of asynchronous updating. Moreover, the effects of variation of the degree of asynchronocity have been investigated and it is observed that the size of the synchronized fixed point window strongly depends on the degree of asynchronocity. The value of coupling constant at the point of onset of synchronization is found analytically and the result is in good agreement with the numerics. Lattice size also has a significant impact on the synchronization behavior for some coupling function. On the other hand in a globally coupled network, synchronization is identified for a certain range of the degree of asynchronocity but surprisingly the width of synchronized fixed point window is independent of the value of the asynchronocity parameter. This study may be useful to explain the spatiotemporal order structure observed in spatially extended complex biological and social systems with the help of stochastic asynchronous updating.