Noise-induced strong stabilization

TL;DR

This paper investigates how stochastic noise can stabilize a 2D system that would otherwise explode in finite time, showing the existence of a random attractor under certain parameters.

Contribution

It demonstrates that stochastic perturbations can induce strong stabilization and the existence of a random attractor in systems prone to finite-time explosion.

Findings

Deterministic system explodes in finite time under certain parameters.

Stochastic system remains strongly complete and admits a random attractor.

Noise induces stabilization in systems that are unstable deterministically.

Abstract

We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes in finite time, but the random dynamical system corresponding to the stochastic equation is not only strongly complete but even admits a random attractor.