Universality and scaling in networks of period-doubling maps with a pacemaker

Ivanova, Anna S.; Kuznetsov, Sergey P.; Osbaldestin, Andrew H.

doi:https://doi.org/10.1155/DDNS/2006/74723

Discrete Dynamics in Nature and Society

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Volume 2006 | Article ID 074723 | https://doi.org/10.1155/DDNS/2006/74723

Universality and scaling in networks of period-doubling maps with a pacemaker

Anna S. Ivanova,¹Sergey P. Kuznetsov,²and Andrew H. Osbaldestin³

Received10 Oct 2005

Accepted08 Jan 2006

Published27 Jul 2006

Abstract

The networks of globally coupled maps with a pacemaker have been introduced. We consider a generalization of the Kaneko model with a pacemaker represented by a single period-doubling element coupled unidirectionally with a set of other mutually coupled cells. We also investigate the dynamics of a system of two unidirectionally coupled elements, which manifests a special type of critical behaviour, known as bicriticality, at the point of simultaneous transition to chaos in both subsystems. With the help of the renormalization group (RG), we show for a case of two mutually coupled bicritical maps with a pacemaker that there are two types of coupling: dissipative and inertial. We investigate the dynamics of a network with a pacemaker with two types of global coupling and the properties of universality and scaling in this system.

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Copyright

Copyright © 2006 Anna S. Ivanova et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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