Stochastic differential delay equations of population dynamics

In this paper we stochastically perturb the delay Lotka-Volterra model x˙(t)=diag(x1(t),…,xn(t))[A(x(t)−x¯)+B(x(t−τ)−x¯)] into the stochastic delay differential equation (SDDE) dx(t)=diag(x1(t),…,xn(t)){[A(x(t)−x¯)+B(x(t−τ)−x¯)]dt+σ(x(t)−x¯)dw(t)}. The main aim is to reveal the effects of environmental noise on the delay Lotka-Volterra model. Our results can essentially be divided into two categories: