On Delayed Logistic Equation Driven by Fractional Brownian Motion

Abstract

In this paper we use the fractional stochastic integral given by Carmona (2003,“Stochastic Integration With Respect to Fractional Brownian Motion,” Ann. IHP Probab. Stat., 39 (1), pp. 27–68) to study a delayed logistic equation driven by fractional Brownian motion which is a generalization of the classical delayed logistic equation. We introduce an approximate method to find the explicit expression for the solution. Our proposed method can also be applied to the other models and to illustrate this, two models in physiology are discussed.