2002/07/08 by René Mikkelsen, Mikkelsen, René, Martin van Hecke +3
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0207208
15 pages, 17 Figs, submitted
arxiv created 2002/07/08 · openalex publication_date 2002/07/08 · arxiv updated 2009/11/30 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We study the transition from laminar to chaotic behavior in deterministic\nchaotic coupled map lattices and in an extension of the stochastic\nDomany--Kinzel cellular automaton [DK]. For the deterministic coupled map\nlattices we find evidence that ``solitons'' can change the em nature of the\ntransition: for short soliton lifetimes it is of second order, while for longer\nbut em finite lifetimes, it is more reminiscent of a first order transition.\nIn the second order regime the deterministic model behaves like Directed\nPercolation with infinitely many absorbing states; we present evidence obtained\nfrom the study of bulk properties and the spreading of chaotic seeds in a\nlaminar background. To study the influence of the solitons more specifically,\nwe introduce a soliton including variant of the stochastic Domany--Kinzel\ncellular automaton. Similar to the deterministic model, we find a transition\nfrom second to first order behavior due to the solitons, both in a mean field\nanalysis and in a numerical study of the statistical properties of this\nstochastic model. Our study illustrates that under the appropriate mapping some\ndeterministic chaotic systems behave like stochastic models; but it is hard to\nknow precisely which degrees of freedom need to be included in such\ndescription.\n