Time delay effects on coupled limit cycle oscillators at Hopf bifurcation

Ramana Reddy, D. V. ; Sen, A. ; Johnston, G. L. (1999) Time delay effects on coupled limit cycle oscillators at Hopf bifurcation Physica D: Nonlinear Phenomena, 129 (1-2). pp. 15-34. ISSN 0167-2789

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Official URL: http://www.sciencedirect.com/science/article/pii/S...

Related URL: http://dx.doi.org/10.1016/S0167-2789(99)00004-4


We present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple model consisting of just two oscillators with a time delayed coupling, the bifurcation diagram obtained by numerical and analytical solutions shows significant changes in the stability boundaries of the amplitude death, phase locked and incoherent regions. A novel result is the occurrence of amplitude death even in the absence of a frequency mismatch between the two oscillators. Similar results are obtained for an array of N oscillators with a delayed mean field coupling and the regions of such amplitude death in the parameter space of the coupling strength and time delay are quantified. Some general analytic results for the N→ ∞ (thermodynamic) limit are also obtained and the implications of the time delay effects for physical applications are discussed.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Coupled Oscillators; Time Delay; Hopf Bifurcation; Amplitude Death; Synchronization; Phase Locking
ID Code:85274
Deposited On:02 Mar 2012 07:17
Last Modified:02 Mar 2012 07:17

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