Dynamics of coupled modified Rossler oscillators: the role of nonisochronicity parameter

TL;DR

This paper investigates how nonisochronicity influences the dynamics of coupled Rossler oscillators, revealing new fixed points, coexisting attractors, and complex bifurcation sequences affecting synchronization and oscillation death.

Contribution

It introduces the role of nonisochronicity in coupled Rossler oscillators, highlighting new fixed points, multistability, and bifurcation phenomena not previously characterized.

Findings

Emergence of a new fixed point due to nonisochronicity

Coexistence of limit-cycle and quasiperiodic attractors

Sequence of bifurcations leading to synchronization and oscillation death

Abstract

The amplitude-dependent frequency of the oscillations, termed \emph{nonisochronicity}, is one of the essential characteristics of nonlinear oscillators. In this paper, the dynamics of the Rossler oscillator in the presence of nonisochronicity is examined. In particular, we explore the appearance of a new fixed point and the emergence of a coexisting limit-cycle and quasiperiodic attractors. We also describe the sequence of bifurcations leading to synchronized, desynchronized attractors and oscillation death states in the coupled Rossler oscillators as a function of the strength of nonisochronicity and coupling parameters. Further, we characterize the multistability of the coexisting attractors by plotting the basins of attraction. Our results open up the possibilities of understanding the emergence of coexisting attractors, and into a qualitative change of the collective states in coupled nonlinear oscillators in the presence of nonisochronicity.