Punetha, Nirmal ; Karnatak, Rajat ; Prasad, Awadhesh ; Kurths, Jürgen ; Ramaswamy, Ram (2012) Frequency discontinuity and amplitude death with time-delay asymmetry Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 85 (4). Article ID 046204. ISSN 1539-3755
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Official URL: http://journals.aps.org/pre/abstract/10.1103/PhysR...
Related URL: http://dx.doi.org/10.1103/PhysRevE.85.046204
Abstract
We consider oscillators coupled with asymmetric time delays, namely, when the speed of information transfer is direction dependent. As the coupling parameter is varied, there is a regime of amplitude death within which there is a phase-flip transition. At this transition the frequency changes discontinuously, but unlike the equal delay case when the relative phase difference changes by π, here the phase difference changes by an arbitrary value that depends on the difference in delays. We consider asymmetric delays in coupled Landau-Stuart oscillators and Rössler oscillators. Analytical estimates of phase synchronization frequencies and phase differences are obtained by separating the evolution equations into phase and amplitude components. Eigenvalues and eigenvectors of the Jacobian matrix in the neighborhood of the transition also show an “avoided crossing,” as has been observed in previous studies with symmetric delays.
Item Type: | Article |
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Source: | Copyright of this article belongs to The American Physical Society. |
ID Code: | 98818 |
Deposited On: | 14 May 2015 12:15 |
Last Modified: | 14 May 2015 12:15 |
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