Stability of Stochastic Delay Logistic Model Incorporating Ornstein-Uhlenbeck Process

Tawfiqullah Ayoubi

Abstract: This paper is concerned about the stability of stochastic delay logistic model with Ornsttein-Uhlenbeck process. First, current paper introduces a general theory to determine the stability of SDDEs for zero solution in term of equation (1) via Lyapunov function. Aftermath, this result verified by stochastic logistic model with delayed feedback and several equations. Furthermore, this research uses the 4-stage stochastic Runge-Kutta (SRK4) method to evaluate the numerical solution and reflects the reality of the results.

Keywords: Stability, Ornsttein-Uhlenbeck Process, Logistic model, Stochastic Runge-Kutta method