Additional complex conjugate feedback-induced explosive death and multistabilities

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.

Automated summary

This study investigates the impact of additional complex conjugate feedback on globally coupled Stuart-Landau oscillators, revealing phenomena such as symmetry breaking clusters, out-of-phase clusters, explosive amplitude death, and disparate multistable states. By characterizing the first-order transition and hysteresis nature through the amplitude order parameter, mapping global dynamical transitions in parametric spaces, analyzing bifurcation scenarios of the reduced model, and exploring basin stability, the research sheds light on emergent dynamics in the presence of additional feedback.