Onset of explosive chimera death in coupled oscillators
摘要
This study has uncovered a remarkable dynamical phenomenon termed explosive chimera death in repulsively coupled van der Pol oscillators under parametric perturbation. By introducing an asymmetry parameter that breaks the coupling symmetry between state variables, the numerical simulations show that a moderate level of perturbation fundamentally alters the system’s transition pathway, transforming the continuous quenching observed in the unperturbed case into an abrupt, irreversible collapse. This explosiveness manifests in two distinct forms depending on perturbation strength. For a moderate perturbation strength, the system exhibits explosive chimera death, manifesting as a sudden jump from cluster synchronization directly into a stationary chimera death state, a hybrid regime where coherent and incoherent oscillation death domains coexist, marked by pronounced hysteresis. As perturbation strength increases further, a second explosive behavior named explosive nontrivial amplitude death emerges, which is characterized by a discontinuous transition from complete synchronization to a homogeneous coupling-dependent quenched state. Theoretical analysis via the indirect Lyapunov method successfully captures the critical transition boundaries, showing agreement with numerical simulations. This finding underscores the dual role of parametric perturbation. It not only induces explosiveness but also determines the specific nature of the quenched state, whether inhomogeneous chimera death or homogeneous amplitude death. Beyond deepening the fundamental understanding of oscillation quenching, these insights establish parametric perturbation as a potential tool for the design and regulation of abrupt transitions in both natural and engineered contexts.