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

TL;DR

This paper investigates how solitons influence the nature of transitions to spatio-temporal chaos in coupled map lattices, revealing conditions under which the transition shifts from second to first order and comparing deterministic and stochastic models.

Contribution

It demonstrates that solitons can alter the order of the transition in coupled map lattices and introduces a stochastic model with solitons to analyze this effect.

Findings

Solitons can change the transition from second to first order.

Deterministic coupled map lattices behave like directed percolation in the second order regime.

A stochastic model with solitons exhibits similar transition behavior.

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.