Random periodic solutions of nonautonomous stochastic feedback systems with multiplicative noise

TL;DR

This paper proves the existence and convergence of random periodic solutions in nonautonomous stochastic feedback systems with multiplicative noise, demonstrating their stability and applicability to various biological and ecological models.

Contribution

It establishes the existence of random periodic solutions and their almost sure convergence in nonautonomous stochastic feedback systems with multiplicative noise, a novel theoretical result.

Findings

Existence of random periodic solutions proven

Pull-back trajectories converge to these solutions

Applicable to biological and ecological systems

Abstract

We investigate the dynamical behavior of pull-back trajectories for nonautonomous stochastic feedback systems with multiplicative noise. We proved that there exists a random periodic solution of this system and all pull-back trajectories converge to this random periodic solution as time goes to infinitely almost surely. Our results can be applied to nonautonomous stochastic Goodwin negative feedback system, nonautonomous stochastic Othmer-Tyson positive feedback system and nonautonomous stochastic competitive systems etc.