Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1998-10-20
Physica D 129 (1999) 15-34.
Nonlinear Sciences
Chaotic Dynamics
20 aps formatted revtex pages (including 13 PS figures); Minor changes over the previous version; To be published in Physica D
Scientific paper
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 tending to infinity (thermodynamic) limit are also obtained and the implications of the time delay effects for physical applications are discussed.
Johnston George L.
Ramana Reddy D. V.
Sen Abhijit
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