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      Origin of Complexity and Conditional Predictability in Cellular Automata

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          Abstract

          A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The mechanism is used to construct a cellular automaton model for discrete chimera-like states, where synchrony and incoherence in an ensemble of identical oscillators coexist. The incoherent region is shown to have a periodicity that is three orders of magnitude longer than the period of the synchronous oscillation.

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          Statistical mechanics of cellular automata

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            Phase organization

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              Chimera States for Coupled Oscillators

              Arrays of identical oscillators can display a remarkable spatiotemporal pattern in which phase-locked oscillators coexist with drifting ones. Discovered two years ago, such "chimera states" are believed to be impossible for locally or globally coupled systems; they are peculiar to the intermediate case of nonlocal coupling. Here we present an exact solution for this state, for a ring of phase oscillators coupled by a cosine kernel. We show that the stable chimera state bifurcates from a spatially modulated drift state, and dies in a saddle-node bifurcation with an unstable chimera.
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                Author and article information

                Journal
                04 October 2013
                Article
                10.1103/PhysRevE.88.042814
                1310.1380

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                Phys. Rev. E 88, 042814 (2013)
                7 pages, 5 figures, accepted to Physical Review E
                nlin.CG cond-mat.stat-mech math-ph math.MP

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