Open AccessStochastic delay differential equations of three-species prey-predator system with cooperation among prey species
Author(s) -
Fathalla A. Rihan,
Hebatallah J. Alsakaji
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2020468
Subject(s) - ergodic theory , uniqueness , extinction (optical mineralogy) , predator , predation , mathematics , noise (video) , environmental noise , lyapunov function , stochastic differential equation , stationary distribution , differential equation , statistical physics , control theory (sociology) , ecology , mathematical analysis , biology , statistics , computer science , physics , nonlinear system , paleontology , image (mathematics) , control (management) , quantum mechanics , artificial intelligence , acoustics , markov chain , sound (geography)
Environmental factors and random variation have strong effects on the dynamics of biological and ecological systems. In this paper, we propose a stochastic delay differential model of two-prey, one-predator system with cooperation among prey species against predator. The model has a global positive solution. Sufficient conditions of existence and uniqueness of an ergodic stationary distribution of the positive solution are provided, by constructing suitable Lyapunov functionals. Sufficient conditions for possible extinction of the predator populations are also obtained. The conditions are expressed in terms of a threshold parameter \begin{document}$ {\mathcal R}_0^s $\end{document} that relies on the environmental noise. Illustrative examples and numerical simulations, using Milstein's scheme, are carried out to illustrate the theoretical results. A small scale of noise can promote survival of the species. While relative large noises can lead to possible extinction of the species in such an environment.