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Emergence of collective behavior in dynamical networks

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  • One of the main paradigms of the theory of weakly interacting chaotic systems is the absence of phase transitions in generic situation. We propose a new type of multicomponent systems demonstrating in the weak interaction limit both collective and independent behavior of local components depending on fine properties of the interaction. The model under consideration is related to dynamical networks and sheds a new light to the problem of synchronization under weak interactions.
    Mathematics Subject Classification: 37A60, 37D20, 34C15, 37L60.


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