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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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          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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              Loss of coherence in dynamical networks: spatial chaos and chimera states

              , , (2011)
              We discuss the breakdown of spatial coherence in networks of coupled oscillators with nonlocal interaction. By systematically analyzing the dependence of the spatio-temporal dynamics on the range and strength of coupling, we uncover a dynamical bifurcation scenario for the coherence-incoherence transition which starts with the appearance of narrow layers of incoherence occupying eventually the whole space. Our findings for coupled chaotic and periodic maps as well as for time-continuous R\"ossler systems reveal that intermediate, partially coherent states represent characteristic spatio-temporal patterns at the transition from coherence to incoherence.
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                Author and article information

                Journal
                10.1103/PhysRevE.88.042814
                1310.1380

                Mathematical physics,Condensed matter,Mathematical & Computational physics,Nonlinear & Complex systems

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