Collective stochastic resonance behavior in the globally coupled fractional oscillator

This study investigates the collective stochastic resonance (SR) behavior of globally coupled fractional Langevin equations with multiplicative noise and external signal. We define the mean field S(t) and derive the steady-state output amplitude $A_1$ of the first moment $⟨S\left(t\right)⟩$ by using the stochastic average method. We characterize the effects of fractional order, intrinsic frequency, noise correlation rate, and driving frequency on the steady-state output amplitude $A_1$ as a function of noise intensity. We observe that the collective SR phenomenon occurs in a fractional coupled stochastic dynamic system. We also demonstrate that collective SR behavior versus noise intensity can ensue when system parameters satisfy the necessary and sufficient conditions; this notion means that we can control the collective SR of our fractional dynamic model by properly adjusting the system parameters within a certain range. This study verifies the reliability and effectiveness of the theoretical results by various numerical simulations. Our results on SR in a globally coupled fractional harmonic oscillator provide useful information in modern science.