Behavior of collective variables in complex nonlinear stochastic models of finite size

Abstract

We consider the behavior of a collective variable in a complex system formed by a finite number of interacting subunits. Each of them is characterized by a degree of freedom with an intrinsic nonlinear bistable stochastic dynamics. The lack of ergodicity of the collective variable requires the consideration of a feedback mechanism of the collective behavior on the individual dynamics. We explore numerically this issue within the context of two simple finite models with a feedback mechanism of the Weiss mean-field type: a global coupling model and another one with nearest neighbors coupling.