Collective dynamics of time-delay-coupled phase oscillators in a frustrated geometry

摘要

We study the effect of time delay on the dynamics of a system of repulsively coupled nonlinear oscillators thatare configured as a geometrically frustrated network. In the absence of time delay, frustrated systems are knownto possess a high degree of multistability among a large number of coexisting collective states except for thefully synchronized state that is normally obtained for attractively coupled systems. Time delay in the couplingis found to remove this constraint and to lead to such a synchronized ground state over a range of parametervalues. A quantitative study of the variation of frustration in a system with the amount of time delay has beenmade and a universal scaling behavior is found. The variation in frustration as a function of the product of timedelay and the collective frequency of the system is seen to lie on a characteristic curve that is common for allnatural frequencies of the identical oscillators and coupling strengths. Thus time delay can be used as a tuningparameter to control the amount of frustration in a system and thereby influence its collective behavior. Ourresults can be of potential use in a host of practical applications in physical and biological systems in whichfrustrated configurations and time delay are known to coexist.