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ARTICLE

Stability and Bifurcation Analysis of a Discrete Predator-Prey Model with Mixed Holling Interaction

M. F. Elettreby^{1, 2, *}, Tamer Nabil^{1, 3}, A. Khawagi⁴

1 Mathematics Department, Faculty of Science, King Khalid University, Abha, 9004, Saudi Arabia.
2 Mathematics Department, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt.
3 Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt.
4 Mathematics Department, Faculty of Science and Arts, King Khalid University, Mohayil Asir, Saudi Arabia.

* Corresponding Author: M. F. Elettreby. Email: .

Computer Modeling in Engineering & Sciences 2020, 122(3), 907-921. https://doi.org/10.32604/cmes.2020.08664

Received 24 September 2019; Accepted 10 January 2020; Issue published 01 March 2020

Abstract

In this paper, a discrete Lotka-Volterra predator-prey model is proposed that considers mixed functional responses of Holling types I and III. The equilibrium points of the model are obtained, and their stability is tested. The dynamical behavior of this model is studied according to the change of the control parameters. We find that the complex dynamical behavior extends from a stable state to chaotic attractors. Finally, the analytical results are clarified by some numerical simulations.

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Citations