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 [E. Domany and W. Kinzel, Phys. Rev. Lett. 53, 311 (1984)]. For the deterministic coupled map lattices, we find evidence that ¿solitons¿ can change the nature of the transition: for short soliton lifetimes it is of second order, while for longer but 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.
|Number of pages||13|
|Journal||Physical review E: Statistical physics, plasmas, fluids, and related interdisciplinary topics|
|Publication status||Published - 2003|
Mikkelsen, R., van Hecke, M., & Bohr, T. (2003). Influence of solitions on the transition to spatiotemporal chaos in coupled map lattices. Physical review E: Statistical physics, plasmas, fluids, and related interdisciplinary topics, 67(4), . https://doi.org/10.1103/PhysRevE.67.046207