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Journal of Applied Nonlinear Dynamics 13(2) (2024) 191--202 | DOI:10.5890/JAND.2024.06.001

Mahmoud Moustafa$^{1,2}$, Suad Mawloud Zali$^3$, Sharidan Shafie$^2$

$^1$ Department of Computer Science, College of Engineering and Information Technology, Onaizah Colleges, Qassim, Saudi Arabia

$^2$ Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, Malaysia

$^3$ Mathematics Department, Faculty of Science, Sabratha University, Sabratha, Libya

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Abstract

In this paper an eco-epidemiological model with fading memory for Holling type II functional response is formulated and analyzed.~The fading memory property is that the predator's present growth rate is dependent on past quantities of prey.~The existence, uniqueness, positivity and boundedness of the solutions of the proposed model are investigated. The local asymptotic stability of obtained equilibrium points are discussed. The analytical condition for Hopf bifurcation around the interior equilibrium point of the proposed system is determined. The proposed model undergoes supercritical Hopf bifurcation. Numerical simulations are performed to clarify the characteristics of the obtained analytical results and understand the effects of fading memory on the dynamics of the proposed model. It is observed that varying the fading memory parameter has a sensitive effect on the model dynamics.

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