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Dynamical analysis of a stochastic three-species predator–prey system with distributed delays

Authors
  • Zhao, Jinxing1
  • Shao, Yuanfu2
  • 1 Inner Mongolia University, Hohhot, 010021, China , Hohhot (China)
  • 2 Guilin University of Technology, Guilin, 541004, China , Guilin (China)
Type
Published Article
Journal
Advances in Difference Equations
Publisher
Springer International Publishing
Publication Date
Jul 22, 2021
Volume
2021
Issue
1
Identifiers
DOI: 10.1186/s13662-021-03493-8
Source
Springer Nature
Keywords
Disciplines
  • Research
License
Green

Abstract

A stochastic two-prey one-predator system with distributed delays is proposed in this paper. Firstly, applying the linear chain technique, we transform the predator–prey system with distributed delays to an equivalent system with no delays. Then, by use of the comparison method and the inequality technique, we investigate the stability in mean and extinction of species. Further, by constructing some suitable functionals, using M-matrix theory and three important lemmas, we establish sufficient conditions assuring the existence of distribution and the attractivity of solutions. Finally, some numerical simulations are given to illustrate the main results.

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