Analysis of a stochastic single species model with Allee effect and jump-diffusion

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 stochas...

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Bibliographic Details
Published in:Advances in difference equations 2020-04, Vol.2020 (1), p.1-11, Article 165
Main Author: Jin, Yalin
Format: Article
Language:English
Subjects:
Allee effect
Analysis
Computer simulation
Difference and Functional Equations
Diffusion effects
Extinction
Functional Analysis
Lévy jumps
Mathematical models
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Stochastic permanence
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Summary: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.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-02631-y