Abstract
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.
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Afraimovich, V.S., Bunimovich, L.A. & Moreno, S.V. Dynamical networks: Continuous time and general discrete time models. Regul. Chaot. Dyn. 15, 127–145 (2010). https://doi.org/10.1134/S1560354710020036
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DOI: https://doi.org/10.1134/S1560354710020036