Abstract
In this paper, we consider the effects of the small and abrupt random perturbations in the environment, and formulate a stochastic single species model with Allee effect and jump-diffusion. We first prove that the model admits a unique solution which is global and positive. Then we study the stochastic permanence and extinction of the model. In addition, we estimate the growth rate of the solution. Our results reveal that the properties of the model have close relationships with the jump-diffusion. Finally, we work out several numerical simulations to validate the theoretical results.
Highlights
In the natural world, plenty of species exhibit the Allee effect [7], for instance, meerkats [6] and the African wild dogs [4]
5 Conclusions and simulations In this paper, we utilized a Lévy jump process to characterize the abrupt perturbations in the environment, and formulated a stochastic single species model with Allee effect and jump-diffusion
We proved that the model admits a unique solution which is global and positive, and investigated the stochastic permanence, extinction and the growth rate of the solution
Summary
Plenty of species exhibit the Allee effect [7], for instance, meerkats [6] and the African wild dogs [4]. In [9, 26] the authors researched the following stochastic single species Where B(t) stands for a standard Brownian motion defined on a completed probability space (Ω, F , P), ξ represents the intensity of the stochastic perturbations. The authors of [26] investigated the persistence, extinction, stochastic permanence and the ergodicity of model (2).
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