Time Delay Effects on Coupled Limit Cycle Oscillators at Hopf Bifurcation
摘要
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.
引用
@article{arxiv.chao-dyn/9810023,
title = {Time Delay Effects on Coupled Limit Cycle Oscillators at Hopf Bifurcation},
author = {D. V. Ramana Reddy and A. Sen and G. L. Johnston},
journal= {arXiv preprint arXiv:chao-dyn/9810023},
year = {2009}
}
备注
20 aps formatted revtex pages (including 13 PS figures); Minor changes over the previous version; To be published in Physica D