Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 74723, 19 pages

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

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

1Department of Nonlinear Processes, Saratov State University, Astrakhanskaya 83, Saratov 410026, Russia
2Laboratory of Theoretical Nonlinear Dynamics, Saratov Branch of Institute of Radio-Engineering and Electronics, Russian Academy of Sciences, Zelenaya 38, Saratov 410019, Russia
3Department of Mathematics, University of Portsmouth, Portsmouth PO1 3HE, UK

Received 10 October 2005; Accepted 8 January 2006

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.


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.