ON DYNAMIC BEHAVIOR OF A DISCRETE FRACTIONAL-ORDER NONLINEAR PREY–PREDATOR MODEL

A. Aldurayhim, A. A. Elsadany and A. Elsonbaty
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A. Aldurayhim: Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
A. A. Elsadany: Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia†Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt
A. Elsonbaty: Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia‡Department of Engineering Mathematics and Physics, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt

FRACTALS (fractals), 2021, vol. 29, issue 08, 1-20

Abstract: This work is devoted to explore the dynamics of the proposed discrete fractional-order prey–predator model. The model is the generalization of the conventional discrete prey–predator model to its corresponding fractional-order counterpart. The fixed points of the proposed model are first found and their stability analyses are carried out. Then, the nonlinear dynamical behaviors of the model, including quasi-periodicity and chaotic behaviors, are investigated. The influences of fractional order and different parameters in the model are examined using several techniques such as Lyapunov exponents, bifurcation diagrams, phase portraits and C0 complexity. The feedback control method is suggested to suppress the chaotic dynamics of the model and stabilize any selected unstable fixed point of the system.

Keywords: Fractional Prey–Predator Map; Caputo-Like Delta Difference; Feedback Control; Chaos Suppression (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21400375

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