Amplitude death in systems of coupled oscillators with distributed-delay coupling

Kyrychko, Yuliya, Blyuss, Konstantin and Schöll, E (2011) Amplitude death in systems of coupled oscillators with distributed-delay coupling. European Physical Journal B: Condensed Matter and Complex Systems, 84 (2). pp. 307-315. ISSN 1434-6028

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Abstract

This paper studies the effects of coupling with distributed delay on the suppression of oscillations in a system of coupled Stuart-Landau oscillators. Conditions for amplitude death are obtained in terms of strength and phase of the coupling, as well as the mean time delay and the width of the delay distribution for uniform and gamma distributions. Analytical results are confirmed by numerical computation of the eigenvalues of the corresponding characteristic equations. These results indicate that larger widths of delay
distribution increase the regions of amplitude death in the parameter space. In the case of a uniformly distributed delay kernel, for sufficiently large width of the delay distribution it is possible to achieve amplitude death for an arbitrary value of the average time delay, provided that the coupling strength has a value in the appropriate range. For a gamma distribution of delay, amplitude death is also possible for an arbitrary value of the average time delay, provided that it exceeds a certain value as determined by the
coupling phase and the power law of the distribution. The coupling phase has a destabilizing effect and reduces the regions of amplitude death.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Konstantin Blyuss
Date Deposited: 08 Nov 2012 11:52
Last Modified: 14 Nov 2012 09:44
URI: http://sro.sussex.ac.uk/id/eprint/41421
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