Non-Maxwellian distribution in linear systems and its applications

Abstract Bimodality is a typical behavior of bistable nonlinear stochastic differential equations. In this work, we find an exact result for calculating the dynamical and stationary probability distribution function in a simple linear system driven by an asymmetric Markovian dichotomous noise. The results show that asymmetric dichotomous noise leads to a unimodal-bimodal distribution transition, exhibiting eight different non-Maxwellian stationary probability distribution profiles in the parameter space. The noise-induced transitions depend on the correlation time, which characterizes the asymmetric dichotomous noise. The calculations are performed using a linear configuration; but applications to other systems governed by nonlinear equations such as single species population growth models are discussed. In the proper limits, the symmetric case, including the Gaussian white noise limit, is recovered. Numerical simulations show good agreement with analytical results. Finally, a possible experimental setup is proposed.