Noised induced phase transition in an oscillatory system with dynamical traps

TL;DR

This paper introduces a novel noised induced phase transition in oscillatory systems with dynamical traps, where noise and trap asymmetry lead to a change in system behavior, analyzed through numerical simulations.

Contribution

It proposes and analyzes a new type of phase transition caused by noise in systems with dynamical traps, highlighting the role of asymmetry in residence time distribution.

Findings

Phase transition caused by noise in systems with dynamical traps.

Asymmetry in residence time distribution near zero velocity.

Numerical analysis confirms the proposed mechanism.

Abstract

A new type of noised induced phase transitions is proposed. It occurs in noisy systems with dynamical traps. Dynamical traps are regions in the phase space where the regular forces are depressed substantially. By way of an example, a simple oscillatory system {x,v} with additive white noise is considered and its dynamics is analyzed numerically. The dynamical trap region is assumed to be located near the x-axis where the velocity v of the system becomes sufficiently low. The meaning of this assumption is discussed. The observed phase transition is caused by the asymmetry in the residence time distribution in the vicinity of zero value velocity. This asymmetry is due to a cooperative effect of the random Langevin force in the trap region and the regular force not changing the direction of action when crossing the trap region.