Universal and non-universal properties of transitions to spatio-temporal chaos in coupled map lattices

René Mikkelsen; Martin van Hecke; Tomas Bohr

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Universal and non-universal properties of transitions to spatio-temporal chaos in coupled map lattices

René Mikkelsen·Martin van Hecke·Tomas Bohr

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Abstract

We study the transition from laminar to chaotic behavior in deterministic chaotic coupled map lattices and in an extension of the stochastic Domany--Kinzel cellular automaton [DK]. For the deterministic coupled map lattices we find evidence that ``solitons'' can change the {\em nature} of the transition: for short soliton lifetimes it is of second order, while for longer but {\em finite} lifetimes, it is more reminiscent of a first order transition. In the second order regime the deterministic model behaves like Directed Percolation with infinitely many absorbing states; we present evidence obtained from the study of bulk properties and the spreading of chaotic seeds in a laminar background. To study the influence of the solitons more specifically, we introduce a soliton including variant of the stochastic Domany--Kinzel cellular automaton. Similar to the deterministic model, we find a transition from second to first order behavior due to the solitons, both in a mean field analysis and in a numerical study of the statistical properties of this stochastic model. Our study illustrates that under the appropriate mapping some deterministic chaotic systems behave like stochastic models; but it is hard to know precisely which degrees of freedom need to be included in such description.

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BibTeX RIS

René Mikkelsen, Martin van Hecke, Tomas Bohr. 2002-07-08. Universal and non-universal properties of transitions to spatio-temporal chaos in coupled map lattices. https://arxiv.org/abs/cond-mat/0207208

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