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 sy...
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| Format: | Article |
| Language: | English |
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Wiley
2006-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/DDNS/2006/74723 |
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| author | Anna S. Ivanova Sergey P. Kuznetsov Andrew H. Osbaldestin |
| author_facet | Anna S. Ivanova Sergey P. Kuznetsov Andrew H. Osbaldestin |
| author_sort | Anna S. Ivanova |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-0bede5f5ffd34da2be5a339dc3010916 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2006-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-0bede5f5ffd34da2be5a339dc30109162025-02-03T01:26:35ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2006-01-01200610.1155/DDNS/2006/7472374723Universality and scaling in networks of period-doubling maps with a pacemakerAnna S. Ivanova0Sergey P. Kuznetsov1Andrew H. Osbaldestin2Department of Nonlinear Processes, Saratov State University, Astrakhanskaya 83, Saratov 410026, RussiaLaboratory of Theoretical Nonlinear Dynamics, Saratov Branch of Institute of Radio-Engineering and Electronics, Russian Academy of Sciences, Zelenaya 38, Saratov 410019, RussiaDepartment of Mathematics, University of Portsmouth, Portsmouth PO1 3HE, UKThe 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.http://dx.doi.org/10.1155/DDNS/2006/74723 |
| spellingShingle | 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 |
| title | Universality and scaling in networks of period-doubling maps with a pacemaker |
| title_full | Universality and scaling in networks of period-doubling maps with a pacemaker |
| title_fullStr | Universality and scaling in networks of period-doubling maps with a pacemaker |
| title_full_unstemmed | Universality and scaling in networks of period-doubling maps with a pacemaker |
| title_short | Universality and scaling in networks of period-doubling maps with a pacemaker |
| title_sort | universality and scaling in networks of period doubling maps with a pacemaker |
| url | http://dx.doi.org/10.1155/DDNS/2006/74723 |
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