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

Anna S. Ivanova, Sergey P. Kuznetsov, Andrew H. Osbaldestin
2006 Discrete Dynamics in Nature and Society  
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 asbicriticality, at the point of simultaneous transition to chaos in both subsystems. With
more » ... 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.
doi:10.1155/ddns/2006/74723 fatcat:d3gzzz6wpvborcghh5t6cjq4cq