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Synchronization of autonomous chaotic networks with far bounds


V.V. Chibissov

Ensembles of coupled maps are known to be common models for studying the dynamics of systems, consisting from plenty of elements. Considerable attention was paid to one-dimensional chains of maps, ensembles with symmetric global bounds, ensembles of maps in a two-dimensional lattice with local bonds. In particular, it was shown that for two-dimensional lattices of maps with local bonds there is no synchronous mode. This behavior is associated with the occurrence of the «on-off» intermittency phenomenon. As a rule, in works on chains and lattices of maps two types of connections were studied: global and local (links only with element’s nearest neighbors). However, both from a theoretical and practical point of view, other bonds configurations, which provide homogeneous states, are also of interest. And if these homogeneous states are stable, chaotic synchronization occurs. In this paper we investigate the dynamics of ensembles of chaotic elements located at the nodes of a square grid in the presence of both local and long-distance links. This model describes an autonomous ensemble, where each element has eight local connections (with the nearest neighbors) and G far bonds total weight γ with elements selected at random. We plotted the minimum number G0 of long-distance bonds, required for synchronization, on the ensemble size. For sufficiently strong bonds, G0 is limited. Weaker bonds cause G0 infinite growth with the size of the ensemble increases. After a further reduction synchronization is not observed.
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