Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators

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Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators

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dc.contributor.author Ashwin, Peter en_GB
dc.contributor.author Dangelmayr, Gerhard en_GB
dc.contributor.department University of Exeter en_GB
dc.contributor.department Colorado State University en_GB
dc.date.accessioned 2008-03-20T13:46:36Z en_GB
dc.date.accessioned 2011-01-25T10:33:52Z en_US
dc.date.accessioned 2013-03-20T12:31:49Z
dc.date.issued 2005 en_GB
dc.description.abstract Systems of coupled oscillators may exhibit spontaneous dynamical formation of attracting synchronized clusters with broken symmetry; this can be helpful in modelling various physical processes. Analytical computation of the stability of synchronized cluster states is usually impossible for arbitrary nonlinear oscillators. In this paper we examine a particular class of strongly nonlinear oscillators that are analytically tractable. We examine the effect of isochronicity (a turning point in the dependence of period on energy) of periodic oscillators on clustered states of globally coupled oscillator networks. We extend previous work on networks of weakly dissipative globally coupled nonlinear Hamiltonian oscillators to give conditions for the existence and stability of certain clustered periodic states under the assumption that dissipation and coupling are small and of similar order. This is verified by numerical simulations on an example system of oscillators that are weakly dissipative perturbations of a planar Hamiltonian oscillator with a quartic potential. Finally we use the reduced phase-energy model derived from the weakly dissipative case to motivate a new class of phase-energy models that can be usefully employed for understanding effects such as clustering and torus breakup in more general coupled oscillator systems. We see that the property of isochronicity usefully generalizes to such systems, and we examine some examples of their attracting dynamics. en_GB
dc.identifier.citation 20 (3), pp. 333-367 en_GB
dc.identifier.doi 10.1080/14689360500151813 en_GB
dc.identifier.uri http://hdl.handle.net/10036/21254 en_GB
dc.language.iso en en_GB
dc.publisher Taylor & Francis en_GB
dc.relation.url http://dx.doi.org/10.1080/14689360500151813 en_GB
dc.subject nonlinear oscillators en_GB
dc.subject symmetry en_GB
dc.subject dynamics en_GB
dc.subject oscillators, electric en_GB
dc.subject electric machinery en_GB
dc.title Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators en_GB
dc.type Article en_GB
dc.type Preprint en_GB
dc.date.available 2008-03-20T13:46:36Z en_GB
dc.date.available 2011-01-25T10:33:52Z en_US
dc.date.available 2013-03-20T12:31:49Z
dc.identifier.issn 1468-9367 en_GB
dc.identifier.issn 1468-9375 en_GB
dc.description This is a preprint of an article whose final and definitive form has been published in DYNAMICAL SYSTEMS © 2005 copyright Taylor & Francis; DYNAMICAL SYSTEMS is available online at: http://www.informaworld.com/openurl?genre=article&issn=1468-9367&volume=20&issue=3&spage=333 en_GB
dc.identifier.journal Dynamical Systems en_GB


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