Finite size fluctuations and stochastic resonance in globally coupled bistable systems

Abstract

The dynamics of a system formed by a finite number $N$ of globally coupled bistable oscillators and driven by external forces is studied focusing on a global variable defined as the arithmetic mean of each oscillator variable. Several models based on truncation schemes of a hierarchy of stochastic equations for a set of fluctuating cumulant variables are presented. This hierarchy is derived using Itô stochastic calculus, and the noise terms in it are treated using an asymptotic approximation valid for large $N$. In addition, a simplified one-variable model based on an effective potential is also considered. These models are tested in the framework of the phenomenon of stochastic resonance. In turn, they are used to explain in simple terms the very large gains recently observed in these finite systems.

References in corpus (6)

• System size resonance in coupled noisy systems and in the Ising model
• Two-state theory of nonlinear Stochastic Resonance
• Macroscopic limit cycle via pure noise-induced phase transition
• High-frequency effects in the FitzHugh-Nagumo neuron model
• Stochastic resonance with weak monochromatic driving: gains above unity induced by high-frequency signals
• Very large stochastic resonance gains in finite sets of interacting identical subsystems driven by subthreshold rectangular pulses

Cited by in corpus (6)

• On the Gaussian approximation for master equations
• Stochastic resonance in finite arrays of bistable elements with local coupling
• The role of fluctuations in the response of coupled bistable units to weak driving time-periodic forces
• Statistical Mechanics of finite arrays of coupled bistable elements
• Diffusive coupling facilitates and impedes noise-induced escape in interacting bistable elements
• A comparative study of asymmetric dichotomous noise and symmetric trichotomous noise induced stochastic resonance in the globally coupled fractional oscillators