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Quasiperiodic, periodic, and slowing-down states of coupled heteroclinic cycles

Li, Dong and Cross, M. C. and Zhou, Changsong and Zheng, Zhigang (2012) Quasiperiodic, periodic, and slowing-down states of coupled heteroclinic cycles. Physical Review E, 85 (1). 016215 . ISSN 1539-3755. http://resolver.caltech.edu/CaltechAUTHORS:20120302-134815034

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Abstract

We investigate two coupled oscillators, each of which shows an attracting heteroclinic cycle in the absence of coupling. The two heteroclinic cycles are nonidentical. Weak coupling can lead to the elimination of the slowing-down state that asymptotically approaches the heteroclinic cycle for a single cycle, giving rise to either quasiperiodic motion with separate frequencies from the two cycles or periodic motion in which the two cycles are synchronized. The synchronization transition, which occurs via a Hopf bifurcation, is not induced by the commensurability of the two cycle frequencies but rather by the disappearance of the weaker frequency oscillation. For even larger coupling the motion changes via a resonant heteroclinic bifurcation to a slowing-down state corresponding to a single attracting heteroclinic orbit. Coexistence of multiple attractors can be found for some parameter regions. These results are of interest in ecological, sociological, neuronal, and other dynamical systems, which have the structure of coupled heteroclinic cycles.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevE.85.016215DOIUNSPECIFIED
http://link.aps.org/doi/10.1103/PhysRevE.85.016215PublisherUNSPECIFIED
Additional Information:© 2012 American Physical Society. Received 6 July 2011; revised 28 November 2011; published 30 January 2012. The authors acknowledge Grigory Osipov for useful discussions. This work is supported in part by the National Natural Science Foundation of China, the 973 Program, the Foundation of Doctoral Training, and the Fundamental Research Funds for the Central Universities. M.C.C. thanks Beijing Normal University for support and hospitality during the initial stages of this work. C.Z. is supported by Hong Kong Baptist University.
Funders:
Funding AgencyGrant Number
National Natural Science Foundation of ChinaUNSPECIFIED
973 ProgramUNSPECIFIED
Foundation of Doctoral TrainingUNSPECIFIED
Fundamental Research Funds for the Central UniversitiesUNSPECIFIED
Beijing Normal UniversityUNSPECIFIED
Hong Kong Baptist UniversityUNSPECIFIED
Classification Code:PACS: 05.45.Xt
Record Number:CaltechAUTHORS:20120302-134815034
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120302-134815034
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29568
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:13 Mar 2012 17:30
Last Modified:26 Dec 2012 14:54

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