Time scale governs explosive transitions in two-layer multiplex networks

This study investigates the mechanism of explosive oscillation quenching in a two-layer network where oscillators interact with an environmental layer via feedback coupling, with particular focus on how dynamic time scale governs transitions between bistable regimes. It is demonstrated that significant time scale differences induce and enhance explosive nontrivial amplitude death, characterized by prominent hysteresis and emergent bistability between complete synchronization and nontrivial amplitude death. As the time scale parameter varies, the system evolves through multiple dynamical regimes, including semi hysteresis region where amplitude death and nontrivial amplitude death coexist. Furthermore, the work establishes that both the hysteresis associated with explosive death and subsequent multistability regions can be systematically controlled by adjusting the time scale parameter. Moreover, the analysis reveals that strong inter-layer coupling facilitates multistability, while the damping coefficient and intrinsic frequency collectively regulate the accessibility of explosive versus continuous transitions. Theoretical stability boundaries derived through Lyapunov analysis show excellent agreement with numerical simulations, validating the proposed mechanisms. This work elucidates the fundamental principles governing explosive oscillations and multistability in multilayer networks, thus providing a new understanding of oscillation control mechanisms, which proves essential for manipulating dynamical behaviors through time scale tuning.