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Zohreh Eskandari, Parvaiz Ahmad Naik, Mehmet Yavuz. DYNAMICAL BEHAVIORS OF A DISCRETE-TIME PREY-PREDATOR MODEL WITH HARVESTING EFFECT ON THE PREDATOR[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 283-297. doi: 10.11948/20230212
Citation: Zohreh Eskandari, Parvaiz Ahmad Naik, Mehmet Yavuz. DYNAMICAL BEHAVIORS OF A DISCRETE-TIME PREY-PREDATOR MODEL WITH HARVESTING EFFECT ON THE PREDATOR[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 283-297. doi: 10.11948/20230212
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DYNAMICAL BEHAVIORS OF A DISCRETE-TIME PREY-PREDATOR MODEL WITH HARVESTING EFFECT ON THE PREDATOR

  • 1.

    Department of Mathematics, Faculty of Science, Fasa University, Fasa, Iran

  • 2.

    Department of Mathematics and Computer Science, Youjiang Medical University for Nationalities, Baise, Guangxi, China

  • 3.

    Department of Mathematics and Computer Sciences, Faculty of Science, Necmettin Erbakan University, Konya, Turkey

    Abstract

  • This study investigates the dynamics of a discrete-time prey-predator model with a harvesting effect on the predator. During the analysis of the bifurcations at the interior fixed point, we find that there are some generic bifurcations, including fold, flip, Neimark-Sacker, and strong resonance bifurcations. Using the normal form theory and the center manifold theorem, we can characterize these bifurcations. Furthermore, we determine the non-degeneracy conditions for the computed bifurcations and compute the critical normal form coefficients. Our analysis of the obtained analytical results as well as the revealing of more complex dynamical behaviors that cannot be achieved analytically is carried out using the numerical continuation method by computing several bifurcation curves emanating from the detected bifurcation points.

    MSC: 37G35, 39A30, 39A33, 91B76, 92B05, 92D25
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