Dynamics of coupled modified Rössler oscillators: The role of nonisochronicity parameter

Abstract

The amplitude-dependent frequency of the oscillations, termed nonisochronicity, is one of the essential characteristics of nonlinear oscillators. In this paper, the dynamics of the Rössler 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 Rössler oscillators as a function of the strength of nonisochronicity and coupling parameters. Furthermore, 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.