Stabilization of causally and non-causally coupled map lattices

Details Stabilization of causally and non-causally coupled map lattices Stabilization of causally and non-causally coupled map lattices

2004-07-07

arxiv.org/abs/nlin/0407011v1

Physica A 345 (2005) 435-447

Nonlinear Sciences

Chaotic Dynamics

15 pages, 5 figures, accepted for publication in Physica A

Scientific paper

Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of "causal" coupling (to spatially distant past states) or "non-causal" coupling (to spatially distant simultaneous states). In this contribution we show that globally stable behavior of coupled map lattices is facilitated by causal coupling, thus indicating a surprising relationship between stability and causality. The influence of causal versus non-causal coupling for synchronous and asynchronous updating as a function of coupling strength and for different neighborhoods is analyzed in detail.

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