Edge of Spatial Chaos in Nonlinear Networks with Local Connections

6th IEEE International Specialist Workshop on Nonlinear Dynamics of Electronic Systems, Budapest, Hungary, 16-18 July, 1998

EDGE OF SPATIAL CHAOS IN NONLINEAR NETWORKS WITH LOCAL CONNECTIONS

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

Proceedings of the 6th IEEE International Specialist Workshop on Nonlinear Dynamics of Electronic Systems, Budapest, Hungary, 16-18 July, 1998, pp. 145-148

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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