Some new results on the dynamical behavior of non-autonomous logistic system with random perturbation

TL;DR

This paper investigates how stochastic perturbations influence the dynamics of a non-autonomous logistic system, revealing conditions under which noise affects stability and long-term behavior.

Contribution

It introduces a new research method for stochastic equations and provides novel sufficient conditions for stability, boundedness, and extinction in stochastic logistic systems.

Findings

Small noise preserves deterministic dynamics

Large noise can disrupt stability

New conditions for stochastic permanence and extinction

Abstract

In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have similar dynamic behave with the deterministic system, but if the noise is sufficiently large, it will spoil these nice properties. Furthermore, we introduce a new research method for studying the stochastic equation and some new sufficient conditions for the stochastic bounded, stochastic permanence, extinction and global attractivity of the system are established. The corresponding results are improved and extended.