Effect of configuration symmetry on synchronization in a Van der Pol ring with nonlocal interactions

Abstract

This paper discusses the influence of configuration symmetry on synchronization of coupled Van der Pol oscillators in a ring, where the inherent symmetry in an even number ring is broken by the presence of an odd oscillator. The coupling is considered to be nonlocal represented with a particular scaling exponent which decays with distance. The effect of initial conditions on synchronization dynamics is also studied.Synchronization in such ring networks is tracked from sets of initial conditions having periodic solutions. The set of these typical initial conditions is obtained by implementing a new generalized shooting strategy in the ring model. The robustness of this new method will bypass all the transients and give a periodic orbit, if any, for a given arbitrary initial condition. From these periodic initial conditions, interesting dynamics in odd and even number ring such as waking time of odd oscillator, shifting from antiphase to inphase clusters, resurrection of the oscillators from amplitude death, etc., are discussed. Important quantitative effects due to nonlocal interactions and the presence of initial condition-based amplitude death are also detailed.