Collective behaviors in globally coupled harmonic oscillators with fluctuating damping coefficient

In this paper, the collective behaviors in a globally coupled system consisting of harmonic oscillators with damping fluctuation modeled as dichotomous noise are investigated. First, the first and second moments of mean field and the fluctuation of single particle are introduced to describe the collective behaviors of the system. Then, based on the moment method and Shapiro–Loginov formula, the stability conditions for the coupled system and the analytical expressions for the output amplitude are obtained. Finally, according to the analytical expressions and numerical simulations based on the stochastic Taylor expansion, the collective behaviors are discussed, including synchronization and stochastic resonance. Stationary regime plays an important role in this coupled system. In the stationary regime, all the particles move synchronously and the output amplitudes are bounded which can be reliably estimated, whereas in the non-stationary regime, the first moment cannot be reliably estimated and the distribution of realizations is characterized by fat tail.