Dynamical networks: continuous time and general discrete time models

    2010, Volume 15, Numbers 2-3, pp.  127-145

    Author(s): Afraimovich V. S., Bunimovich L. A., Moreno S. V.

    Dynamical networks are characterized by 1) their topology (structure of the graph of interactions among the elements of a network); 2) the interactions between the elements of the network; 3) the intrinsic (local) dynamics of the elements of the network. A general approach to studying the commulative effect of all these three factors on the evolution of networks of a very general type has been developed in [1]. Besides, in this paper there were obtained sufficient conditions for a global stability (generalized strong synchronization) of networks with an arbitrary topology and the dynamics which is a composition (action of one after another) of a local dynamics of the elements of a network and of the interactions between these elements. Here we extend the results of [1] on global stability (generalized strong synchronization) to the case of a general dynamics in discrete time dynamical networks and to general dynamical networks with continuous time.
    Keywords: global stability, topological pressure, topological Markov chain, dynamical networks
    Citation: Afraimovich V. S., Bunimovich L. A., Moreno S. V., Dynamical networks: continuous time and general discrete time models, Regular and Chaotic Dynamics, 2010, Volume 15, Numbers 2-3, pp. 127-145

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