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
Afraimovich V. S., Bunimovich L. A., Moreno S. V.
Dynamical networks: continuous time and general discrete time models
2010, vol. 15, no. 2-3, pp. 127-145
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 . 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  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.