UNSPECIFIED (1992) THE DYNAMICS OF N-WEAKLY COUPLED IDENTICAL OSCILLATORS. JOURNAL OF NONLINEAR SCIENCE, 2 (1). pp. 69-108. ISSN 0938-8974

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Abstract

We present a framework for analysing arbitrary networks of identical dissipative oscillators assuming weak coupling. Using the symmetry of the network, we find dynamically invariant regions in the phase space existing purely by virtue of their spatio-temporal symmetry (the temporal symmetry corresponds to phase shifts). We focus on arrays which are symmetric under all permutations of the oscillators (this arises with global coupling) and also on rings of oscillators with both directed and bidirectional coupling. For these examples, we classify all spatio-temporal symmetries, including limit cycle solutions such as in-phase oscillation and those involving phase shifts. We also show the existence of "submaximal" limit cycle solutions under generic conditions. The canonical invariant region of the phase space is defined and used to investigate the dynamics. We discuss how the limit cycles lose and gain stability, and how symmetry can give rise to structurally stable heteroclinic cycles, a phenomenon not generically found in systems without symmetry. We also investigate how certain types of coupling (including linear coupling between oscillators with symmetric waveforms) can give rise to degenerate behaviour, where the oscillators decouple into smaller groups.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics T Technology > TJ Mechanical engineering and machinery Q Science > QC Physics
Journal or Publication Title:	JOURNAL OF NONLINEAR SCIENCE
Publisher:	SPRINGER VERLAG
ISSN:	0938-8974
Date:	1992
Volume:	2
Number:	1
Number of Pages:	40
Page Range:	pp. 69-108
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/22151

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