Edge of Spatiotemporal Chaos in Cellular Nonlinear Networks

1998 Fifth IEEE International Workshop on CELLULAR NEURAL NETWORKS AND THEIR APPLICATIONS

EDGE OF SPATIOTEMPORAL CHAOS IN CELLULAR NONLINEAR NETWORKS

Alexander S. Dmitriev and Yuri V. Andreyev
Institute of Radioengineering and Electronics of the Russian Academy of Sciences
Mokhovaya st., 11, Moscow, 103907, Russia
Email: chaos@mail.cplire.ru

Proceedings of 1998 Fifth IEEE International Workshop on CELLULAR NEURAL NETWORKS AND THEIR APPLICATIONS, London, England, 14-17 April, 1998, pp. 100-105

Abstract

In this report, we investigate phenomena on the edge of spatially uniform chaotic mode and spatial temporal chaos in a lattice of chaotic 1-D maps with only local connections. It is shown that in autonomous lattice with local connections, spatially uniform chaotic mode cannot exist if the Lyapunov exponent of the isolated chaotic map is greater than some critical value _cr > 0. We proposed a model of a lattice with a pacemaker and found a spatially uniform mode synchronous with the pacemaker, as well as a spatially uniform mode different from the pacemaker mode.

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