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

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 te...

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Bibliographic Details
Published inAdvances in difference equations Vol. 2021; no. 1; pp. 1 - 27
Main Authors Zhao, Jinxing, Shao, Yuanfu
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 22.07.2021
Springer Nature B.V
SpringerOpen
Subjects
Analysis
Difference and Functional Equations
Distributed delay
Distribution
Endangered & extinct species
Extinction
Functional Analysis
Mathematics
Mathematics and Statistics
Matrix theory
Noise
Ordinary Differential Equations
Partial Differential Equations
Population
Predator-prey simulation
Predators
Simulation
Stability in mean
Stability in mean
34A37
Simulation
92B05
Distribution
Distributed delay
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Summary: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.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03493-8