A phase transition in a system driven by coloured noise.

Progress of Theoretical Physics, 1980

By using the formula for the steady state probability distribution o£ fluctuation in a nonlinear :;ystems uncl'er the influence of two-level i'viarkovian noise, the existence of phase transitions of such a system with the variation of intensity and correlation time of the noise is shown. Explicit results for the Verhulst model and a model for population genetics are given and compared with the previous results for the white noise case.

Physics Letters A, 1979

A general method to calculate explicitly the stationary probability of nonlinear systems subjected to a special case of coloured noise is presented. For a simple model system the "phase diagram" for the various noise-induced transitions is determined.

2007

The study of the effect of the noises' statistics and spectrum on second-order, purely noiseinduced phase transition (NIPT) is of wide interest: It is simplified if the noises are dynamically generated by means of stochastic differential equations driven by white noises, a well known case being that of Ornstein-Uhlenbeck noises with a self-correlation time x whose effect on the NIPT phase diagram has been studied some time ago. Another case is when the stationary pdf is a (colored) q-Gaussian which, being a. fat-tail distribution for q > 1 and a compact-support one for q < 1, allows for a controlled study of the effects of the departure from Gaussian statistics. As done with stochastic resonance and other phenomena, we exploit this tool to study-within a simple meanfield approximation-the combined effect on NIPT of the noises' statistics and spectrum. Even for relatively small T, it is shown that whereas for fat-tail noise distributions counteract the effect of self-correlation, compact-support ones enhance it.

New Journal of Physics, 2005

We consider thermal activation in a bistable potential in the presence of correlated (Ornstein-Uhlenbeck) noise. Escape rates are discussed as a function of the correlation time of the noise at a constant variance of the noise. In contrast to a large body of previous work, where the variance of the noise decreases with increasing correlation time of the noise, we find a bell-shaped curve for the escape rate with a vanishing rate at zero and infinite correlation times. We further calculate threshold crossing rates driven by energy-constrained coloured noise.

Physics Letters, 1977

We demonstrate on a chemical model that, even above the critical point, phase transitions can be induced solely by the effect of external noise.

Nukleonika, 2008

In a stochastic framework, macroscopic approaches are sought to describe microscopic interaction between different species. Coloured-noise-induced transitions in stochastic N-species Lotka-Volterra systems are considered ana- lytically as an appropriate model extendable to many natural and nano-technological processes. All the results discussed are computed by means of a dynamical mean-field approximation. It is demonstrated that interplay of coloured noise and interaction intensities of species can generate a variety of cooperation effects, such as discontinuous transitions of the mean population density, noise-induced Hopf bifurcations and relaxation oscillation. The necessary conditions for the cooperation effects are also discussed. Particularly, it is established that, in the case of the Beddington functional response, in certain parameter regions of the model an increase in noise correlation time can cause multiple transitions (more than two) between relaxation oscillatory reg...

2000

Activated escape is investigated for systems that are driven by noise whose power spectrum peaks at a finite frequency. Analytic theory and analog and digital experiments show that the system dynamics during escape exhibit a symmetry-breaking transition as the width of the fluctuational spectral peak is varied. For double-well potentials, even a small asymmetry may result in a parametrically large difference of the activation energies for escape from different wells.

2003

We present a study of the escape time from a metastable state in the presence of colored noise, generated by Ornstein-Uhlenbeck process. We analyze the role of the correlated noise and of unstable initial conditions of an overdamped Brownian particle on the enhancement of the average escape time as a function of the noise intensity. We observe the noise enhanced stability (NES) effect for all the initial unstable states and for all values of the correlation time τc investigated. We can distinguish two dynamical regimes characterized by: (a) a weak correlated noise and (b) a strong correlated noise, depending on the value of τc with respect to the relaxation time. With increasing τc we find : (i) a shift of the maximum of the average escape time towards higher values of noise intensity and an enhancement of the value of this maximum; (ii) a broadening of the NES region, which becomes very large in the strong colored noise regime; (iii) in this regime (b), the absence of the peculiar initial condition xc which separates the set of the initial unstable states lying into the divergency region from those which give only a nonmonotonic behavior of the average escape time. *

Journal of Statistical Physics, 1985

Physica D: Nonlinear Phenomena, 2004

Here we study a noise induced transition when the system is driven by a noise source taken as colored and non-Gaussian. We show -using both, a theoretical approximation and numerical simulations-that there is a shift of the transition as the noise departs from the Gaussian behavior. Also, we confirm the reentrance effect found for colored Gaussian noise and show the behavior of the transition line in the phase-like diagram as the noise departs from Gaussianity in the large correlation time limit.