Additional complex conjugate feedback induced explosive death and multistabilities

TL;DR

This paper investigates how additional complex conjugate feedback influences the dynamics of coupled Stuart-Landau oscillators, revealing symmetry breaking, explosive amplitude death, and multistability phenomena.

Contribution

It introduces the effects of complex conjugate feedback on oscillator networks, highlighting new dynamical states and bifurcation scenarios not previously characterized.

Findings

Discovery of symmetry breaking and out-of-phase clusters

Identification of explosive amplitude death with hysteresis

Mapping of dynamical transitions in parameter space

Abstract

Many natural and man-made systems require suitable feedback to function properly. In this study, we aim to investigate the impact of additional complex conjugate feedback on globally coupled Stuart-Landau oscillators. We find that this additional feedback results in the onset of symmetry breaking clusters and out-of-phase clusters. Interestingly, we also find the existence of explosive amplitude death along with disparate multistable states. We characterize the first-order transition to explosive death through the amplitude order parameter and show that the transition from oscillatory to death state indeed shows a hysteresis nature. Further, we map the global dynamical transitions in the parametric spaces. In addition, to understand the existence of multistabilities and their transitions, we analyze the bifurcation scenarios of the reduced model and also explore their basin stability. Our study will shed light on the emergent dynamics in the presence of additional feedback.