Open AccessThe Dynamics of a Food Web System: Role of a Prey Refuge Depending on Both Species
Author(s) -
Ekhlas Abd Al-Husain Jabr,
Dahlia Khaled Bahlool
Publication year - 2021
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.152
H-Index - 4
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2021.62.2.29
Subject(s) - attractor , uniqueness , lyapunov function , food web , mathematics , predation , equilibrium point , bifurcation , dynamics (music) , control theory (sociology) , boundary (topology) , functional response , biological system , mathematical analysis , ecology , computer science , predator , physics , biology , control (management) , differential equation , quantum mechanics , nonlinear system , artificial intelligence , acoustics
This paper aims to study the role of a prey refuge that depends on both prey and predator species on the dynamics of a food web model. It is assumed that the food transfer among the web levels occurs according to Lotka-Volterra functional response. The solution properties, such as existence, uniqueness, and uniform boundedness, are discussed. The local, as well as the global, stabilities of the solution of the system are investigated. The persistence of the system is studied with the assistance of average Lyapunov function. The local bifurcation conditions that may occur near the equilibrium points are established. Finally, numerical simulation is used to confirm our obtained results. It is observed that the system has only one type of attractors that is a stable point, while periodic dynamics do not exist even on the boundary planes.