Bifurcation analysis and Control in a Discrete-Time Predator-Prey Model with Smith-Type Growth and Monod-Haldane Response

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DOI: https://doi.org/10.28924/2291-8639-24-2026-165
Published: May 29, 2026
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A. A. Elsadany, Abdulaziz Almaslokh, B. Alreshidi, Ibrahim M. E. Abdelstar, Bifurcation analysis and Control in a Discrete-Time Predator-Prey Model with Smith-Type Growth and Monod-Haldane Response, Int. J. Anal. Appl., 24 (2026), 165.

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A. A. Elsadany, Abdulaziz Almaslokh, B. Alreshidi, Ibrahim M. E. Abdelstar

Abstract

This work examines a discrete-time predator-prey model that integrates Smith-type prey development and a Monod-Haldane functional response, which includes density-dependent regulation and non-monotonic predation effects. A thorough dynamical study is performed in three phases. First, the existence and local stability of all biologically viable equilibria extinction, predator-free, and coexistence states are demonstrated, uncovering regimes of extinction, stable coexistence, and oscillatory dynamics. Second, a thorough bifurcation analysis reveals important dynamic transitions, such as flip and Neimark-Sacker bifurcations. Two-parameter diagrams show how ecological factors affect system stability and persistence. We suggest an optimal control technique to control based on the chaos that is showing up in the bifurcation diagrams. For the best solutions, we use Pontryagin’s maximal principle. This lets us use adaptive threshold control to keep the model stable. Finally, the numerical simulations confirmed the theoretical findings.

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