Explosive death in interacting networks under mixed coupling
Abstract
Explosive death —a discontinuous, first-order transition from oscillatory dynamics to a steady state— is investigated in a framework of interacting networks under mixed coupling. Unlike previous studies focused on monolayer topologies, this work explores the interplay between local diffusive coupling among peripheral nodes and their respective hubs, and conjugate (dissimilar variable) interactions between the hubs of different layers. We demonstrate that by tuning the intralayer and interlayer coupling strengths, the system exhibits a sudden collapse of oscillations into a steady state. The generality of this explosive transition is verified across a diverse range of dynamical systems, including the Stuart-Landau limit cycle oscillator, and the Hindmarsh-Rose bursting neuron model with star and scale-free networks. Our results suggest that the combination of star-type or scale-free network connectivity and mismatch in coupling variables provides a robust mechanism for inducing abrupt transitions to quenching in multilayered nonlinear systems within the explored parameter space.