S. Moreno
Universidad Autonoma de San Luis Potosi, Karakorum 1470, Lomas 4a 78220, San Luis Potosi, S.L.P., Mexico
Instituto de Investigacion en Comunicacion Optica,
Universidad Autonoma de San Luis Potosi
Publications:
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Afraimovich V. S., Bunimovich L. A., Moreno S. V.
Dynamical networks: continuous time and general discrete time models
2010, vol. 15, nos. 2-3, pp. 127-145
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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