Anna S. Ivanova, Sergey P. Kuznetsov, Andrew H. Osbaldestin, "Universality and scaling in networks of period-doubling maps with a pacemaker", Discrete Dynamics in Nature and Society, vol. 2006, Article ID 074723, 19 pages, 2006. https://doi.org/10.1155/DDNS/2006/74723
Universality and scaling in networks of period-doubling maps with a pacemaker
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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