Asymptotic Behaviour and Extinction of Delay Lotka-Volterra Model with Jump-Diffusion

摘要

This paper studies the effect of jump-diffusion randomenvironmental perturbations on the asymptotic behaviour and extinction of Lotka-Volterra population dynamics with delays.Thecontributions of this paper lie in the following: (a) to consider delay stochastic differential equation with jumps, we introduce a proper initial data space, in which the initial data may be discontinuous function with downward jumps; (b) we show that the delay stochastic differential equation with jumps associated with our model has a unique global positive solution and give sufficient conditions that ensure stochastically ultimate boundedness, moment average boundedness in time, and asymptotic polynomial growth of ourmodel; (c) the sufficient conditions for the extinction of the system are obtained, which generalized the former results and showed that the sufficiently large random jump magnitudes and intensity (average rate of jump events arrival) may lead to extinction of the population.