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Regular and Chaotic Dynamics, 2010, Volume 15, Issue 2-3, Pages 127–145
DOI: https://doi.org/10.1134/S1560354710020036 (Mi rcd483) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On the 75th birthday of Professor L.P. Shilnikov

Dynamical networks: continuous time and general discrete time models

V. S. Afraimovicha, L. A. Bunimovichb, S. V. Morenoa

a Instituto de Investigación en Comunicacion Óptica, Universidad Autónoma de San Luis Potosí Karakorum 1470, Lomas 4a 78220, San Luis Potosi, S.L.P., México
b ABC Math Program and School of Mathematics, Georgia Institute of Technology Atlanta, GA, 30332-0160, USA
Citations (4)
DOI: https://doi.org/10.1134/S1560354710020036
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.
Keywords: global stability, topological pressure, topological Markov chain, dynamical networks.
Received: 11.12.2009
Accepted: 29.12.2009
Bibliographic databases:
Document Type: Personalia
MSC: 37A50, 37A60
Language: English
Citation: V. S. Afraimovich, L. A. Bunimovich, S. V. Moreno, “Dynamical networks: continuous time and general discrete time models”, Regul. Chaotic Dyn., 15:2-3 (2010), 127–145
Citation in format AMSBIB
\Bibitem{AfrBunMor10}
\by V. S. Afraimovich, L. A. Bunimovich, S. V. Moreno
\paper Dynamical networks: continuous time and general discrete time models
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 2-3
\pages 127--145
\mathnet{http://mi.mathnet.ru/rcd483}
\crossref{https://doi.org/10.1134/S1560354710020036}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2644325}
\zmath{https://zbmath.org/?q=an:1213.37021}
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    • This publication is cited in the following 4 articles:
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