A Note on Stability of Stochastic Logistic Model by Incorporating the Ornstein-Uhlenbeck Process

Abstract

In this research, we first prove that the stochastic logistic model (10) has a positive global solution. Subsequently, we introduce the sufficient conditions for the stochastically stability of the general form of stochastic differential equations (SDEs) in terms of equation (1), for zero solution by using the Lyapunov function. This result is verified via several examples in Appendix A. Besides; we prove that the stochastic logistic model, by incorporating the Ornstein-Uhlenbeck process is stable in zero solution. Furthermore, the simulated results are displayed via the 4-stage stochastic Runge-Kutta (SRK4) numerical method.