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ISSN:2325-6192 (print)
ISSN:2325-6206 (online)
Journal of Environmental Accounting and Management
António Mendes Lopes (editor), Jiazhong Zhang(editor)
António Mendes Lopes (editor)

University of Porto, Portugal

Email: aml@fe.up.pt

Jiazhong Zhang (editor)

School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi Province 710049, China

Fax: +86 29 82668723 Email: jzzhang@mail.xjtu.edu.cn

Global Bifurcation Analysis of Higher Codimension in a Ratio Dependent Predator-Prey Model with Prey Refuge and Constant Yield-Harvesting of Both Species

Journal of Environmental Accounting and Management 11(4) (2023) 375--401 | DOI:10.5890/JEAM.2023.12.002

Nawaj Sarif, Sahabuddin Sarwardi

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Abstract

In this paper, a modified ratio-dependent Bazykin prey-predator model with prey refuge and constant harvesting of both species has been considered. The significant mathematical attributes of the proposed model are studied with the assistance of equilibria, local stability analysis, and bifurcation theory. The model displays a complex dynamics within the prey-predator plane. The existence and stability of possible equilibria are examined. The existence of Hopf bifurcation is obtained by analyzing the associated characteristic equation. The direction of the Hopf-bifurcating periodic solution and its stability are determined by calculating the first Lyapunov coefficient. Also, it has been proven that the proposed model exhibits Bogdanov-Takens bifurcation of codimension two for an appropriate choice of bifurcation parameters and calculating the conventional form. Furthermore, some numerical examples are provided to illustrate the theoretical finding. Lastly, discuss their ecological interpretations.

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