Emergence of collective behavior in      dynamical networks

Michael Blank

doi:10.3934/dcdsb.2013.18.313

Article Contents

2013, Volume 18, Issue 2: 313-329. Doi: 10.3934/dcdsb.2013.18.313

This issue Previous Article Galerkin finite element methods for semilinear elliptic differential inclusions Next Article Optimal control of ODE systems involving a rate independent variational inequality

Emergence of collective behavior in dynamical networks

Michael Blank^1,

1.
Russian Academy of Sci., Inst. for Information Transm. Problems, and Higher School of Economics, Moscow

Received: July 31, 2011

Revised: March 31, 2012

Published: February 2013

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Abstract

One of the main paradigms of the theory of weakly interacting chaotic systems is the absence of phase transitions in generic situation. We propose a new type of multicomponent systems demonstrating in the weak interaction limit both collective and independent behavior of local components depending on fine properties of the interaction. The model under consideration is related to dynamical networks and sheds a new light to the problem of synchronization under weak interactions.

Keywords:

Mathematics Subject Classification: 37A60, 37D20, 34C15, 37L60.

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References

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