Reduced-order dynamics of coupled self-induced stochastic resonance quasiperiodic oscillators driven by varying noise intensities

Noise can induce nontrivial behaviors in systems with multiple timescales. The dynamical reduction of fast-slow systems remains a challenging and intriguing problem. Self-induced stochastic resonance is a noise-induced coherent phenomenon that noise is introduced to the fast dynamics. By applying the embedding phase reduction approach, the synchronization behaviors of two non-identically coupled self-induced stochastic resonance oscillators are investigated. The first passage time distribution on the slow manifolds, which is crucial in the reduced phase equation, is well approximated by the Weibull distribution and is continuously estimated regarding the noise intensity by the polynomial interpolation. The effectiveness of the reduced phase equation is validated by the Monte Carlo simulations. The methods and results may motivate data-based investigations on other multiple timescale systems and experimental findings.