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

it is known that a stochastic dierential equation (sde) induces two probabilisticobjects, namely a diusion process and a stochastic ow. while the diusion process isdetermined by the innitesimal mean and variance given by the coecients of the sde,this is not the case for the stochastic ow induced by the sde. in order to characterize thestochastic ow uniquely the innitesimal covariance give...