Abstract
• This is the first time to investigate the persistence and extinction of stochastic Logistic equation with Ornstein-Uhlenbeck process. • Sufficient conditions for non-persistence are established. • Adequate criteria for stochastic persistence and weak persistence are given. The persistence and extinction (PE) are interesting topics in mathematics. This research analyzed PE of stochastic Logistic equations (SLE) by incorporating the Ornstein-Uhlenbeck process (SLOP) and stochastic delay Logistic equation (SDLE) by incorporating the Ornstein-Uhlenbeck process (SLDOP). Firstly, we proved that SLOP and SLDOP have positive solutions. Likewise, for stochastic permanence (SP), weak persistence in the mean (WPM), non-persistence in the mean (NPM) and extinction, the sufficient conditions are established for SLOP and SLDOP. Subsequently, for numerical simulation we used 4-stage stochastic Runge-Kutta (SRK4) to illustrate the effectiveness of the results.
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