Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting

Mokni, Karima and Ch-Chaoui, Mohamed (2024) Dynamic analysis and Chaos control in a discrete predator-prey model with Holling type IV and nonlinear harvesting. Miskolc Mathematical Notes, 25 (2). pp. 899-919. ISSN 1787-2413

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Abstract

In this paper, we investigate the dynamical behavior of a two dimensional discretized prey predator system. The model is formulated in terms of difference equations and derived by using the higher-order implicit Runge Kutta method with a very small step size to attain a discrete time version of its continuous counterpart. The existence of fixed points as well as their local asymptotic stability are proved. Further, it is shown that the model experiences Neimark-Sacker bifurcation (NSB for short) and the periodic doubling bifurcation (PDB) in a small neighborhood of the coexistence fixed point under certain parametric conditions. This analysis utilizes bifurcation theory and the center manifold theorem. The chaos influenced by NSB is stabilized. Finally, we use numerical simulations and computer analysis to check our theories and show more complex behaviors.

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