Rich dynamics in a stochastic predator-prey model with protection zone for the prey and multiplicative noise applied on both species

In this manuscript, a new approach of a stochastic predator-prey interaction with protection zone for the prey is developed and studied. The considered mathematical model consists of a system of two stochastic differential equations, SDEs, describing the interaction between the prey and predator pop...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear dynamics 2021-11, Vol.106 (3), p.2761-2780
Main Authors: Belabbas, Mustapha, Ouahab, Abdelghani, Souna, Fethi
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Differential equations
Dynamical Systems
Endangered & extinct species
Engineering
Extinction
Liapunov functions
Mathematical models
Mechanical Engineering
Original Paper
Populations
Predator-prey simulation
Predators
Vibration
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this manuscript, a new approach of a stochastic predator-prey interaction with protection zone for the prey is developed and studied. The considered mathematical model consists of a system of two stochastic differential equations, SDEs, describing the interaction between the prey and predator populations where the prey exhibits a social behavior called also by “herd behavior.” First, according to the theory of the SDEs, some properties of the solution are obtained, including: the existence and uniqueness of the global positive solution and the stochastic boundedness of the solutions. Then, the sufficient conditions for the persistence in the mean and the extinction of the species are established, where the extinction criteria are discussed in two different cases, namely, the first case is the survival of the prey population, while the predator population goes extinct; the second case is the extinction of all prey and predator populations. Next, by constructing a suitable stochastic Lyapunov function and under certain parametric restrictions, it has been proved that the system has a unique stationary distribution which is ergodic. Finally, some numerical simulations based on the Milstein’s higher-order scheme are performed to illustrate the theoretical predictions.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-021-06903-4