The local Bifurcation of Dynamic Behavior of Predator-Prey System with Refuge for both Species

Intsar Matlob; Saad   Naji

doi:10.30526/38.1.3461

Authors

Intsar Matlob Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq. https://orcid.org/0009-0002-4001-8873
Saad Naji Department of Mathematics, College of Science for Women, University of Baghdad, Iraq. https://orcid.org/0000-0002-6865-9798

DOI:

https://doi.org/10.30526/38.1.3461

Keywords:

Local bifurcation, predator-pery, stability analysis, Lyapunov's function, ecological, Refuge

Abstract

The main purpose of this paper is to study a predator – prey dynamical system consisting of three species prey, specialized predator and generalist predator namely H (t), I (t) and J (t) respectively, w food web and refuge for the prey and specialized predator population. The consider system has five equilibrium points A₀=(0, 0, 0), A₁=(1, 0, 0), A₂=(h, i, 0), A₃=(h, 0, j), and the positive equilibrium point A₄=(h, i, j) .The stability and bifurcation of the equilibrium points was studied and the main influence was the qualitative behavior of the solution. It was found that A₀ was unstable while the other equilibrium points are stable under condition so we study their bifurcation and we show that A₁,A₂,and A₃ are transcritical while A, is saddle node bifurcation. Numerical simulations were used to illustrate the occurrence of local bifurcation of this model.

Author Biographies

Intsar Matlob, Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq.

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Saad Naji, Department of Mathematics, College of Science for Women, University of Baghdad, Iraq.

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