Abstract
In this paper, a stochastic two-prey one-predator model with S-type distributed time delays and Lévy noises is considered. Using the comparison theorem and Ito’s formula, sufficient conditions of persistence in the mean and extinct for each population are established. Then, conditions of global attractivity and stability in distribution by Barbalat’s conclusion are also obtained. Furthermore, Euler numerical simulation method is given to demonstrate our conclusions.
Highlights
For a long time in the past, many scholars have been working on various biological models
Some authors [4] [5] claimed that the two-species model does not describe a dynamic relationship in the real world
In this paper, based on a three-species model with traditional time delays and white noise, the S-type distributed time delays and Lévy noises are considered in our model
Summary
For a long time in the past, many scholars have been working on various biological models. Liu and Qiu [22] studied an autonomous stochastic predator-prey delay model with white noise. They established sufficient and necessary criteria for persistence in the mean and extinction of predator and prey. Liu and Bai [31] investigated the dynamic of a stochastic model with Lévy noises and studied the stability in distribution of the solutions (SDS) of model by Lyapunov function approach. Motivated by the above analysis, we will add the S-type distributed time delays and Lévy noises into the model to study the dynamic of the real population more accurately. We consider a stochastic three-species model with S-type distributed delays and Lévy noises.
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