Periodic Solutions of the Forest Pest System Via Hopf Bifurcation and Averaging Theory

Kardo Baiz Othman; Azad Ibrahim Amen

doi:10.24996/ijs.2022.63.12.35

Authors

Kardo Baiz Othman Department of Mathematics, College of Basic Education, Salahaddin University - Erbil,Iraq/ Department of Mathematics, Basic Education College, Raparin University - Ranya, Iraq/ Department of Mathematics, Faculty of Science, Soran University - Soran, Erbil, Iraq https://orcid.org/0000-0001-9467-6930
Azad Ibrahim Amen Department of Mathematics, Basic Education College, Raparin University - Ranya, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.12.35

Keywords:

Limit cycles, Hopf bifurcation, Averaging theory, Forest pest system

Abstract

This work aims to analyse the dynamic behaviours of the forest pest system. We confirm the forest pest system in plane for limit cycles bifurcating existence from a Hopf bifurcation under certain conditions by using the first Lyapunov coefficient and the second-order of averaging theory. It is shown that all stationary points in this system have Hopf bifurcation points and provide an estimation of the bifurcating limit cycles.