关键词: coupling diversity, weak signal propagation, bistable oscillators, analytical calculations

Abstract: Coupling diversity significantly shapes signal transmission and enhancement by modulating internal component interactions in nonlinear systems. Existing theoretical studies on coupling diversity have primarily focused on one-dimensional bistable systems, which are limited to single-variable scenarios and simple dynamical behaviors and thus fail to adapt to complex real-world systems or reveal multi-dimensional mechanisms. To address these limitations, the present study extends this investigation to two-dimensional globally coupled bistable systems. The research team explores the law of weak signal propagation in a globally coupled model composed of bistable oscillators, in which the coupling strength between oscillators follows a Gaussian distribution. Through dual verification via numerical simulations and analytical calculations, we confirm that when the coupling diversity is at an intermediate level, a resonance effect is induced within the system. This effect directly causes the system's dynamical properties to bifurcate into three oscillation clusters with significant differences. Such a bifurcation phenomenon can significantly amplify the system's collective response to weak external signals. Specifically, with an increase in the mean coupling strength, the peaks of the spectral amplification factor become higher, and the optimal variance exhibits a right-shifting trend. Notably, this phenomenon stably emerges across different system sizes, demonstrating the robustness of the system. This finding provides a reference for a deeper understanding of the regulatory mechanism of coupling diversity in weak signal propagation.

Key words: coupling diversity, weak signal propagation, bistable oscillators, analytical calculations