Dynamics, bifurcations, and machine learning-based analysis of a nonstandard discrete predator-prey model with predator harvesting

Asifa Tassaddiq; Rizwan Ahmed; Rabab Alharbi; Dalal Khalid Almutairi; Ruhaila Md Kasmani; Youngmoon Lee; Jawad Khan; Asifa Tassaddiq; Rizwan Ahmed; Rabab Alharbi; Dalal Khalid Almutairi; Ruhaila Md Kasmani; Youngmoon Lee; Jawad Khan

doi:10.3934/math.20261137

AIMS Mathematics

2026, Volume 11, Issue 9: 28547-28581. doi: 10.3934/math.20261137

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Research article Special Issues

Dynamics, bifurcations, and machine learning-based analysis of a nonstandard discrete predator-prey model with predator harvesting

1.
Department of Information Technology, College of Computer and Information Sciences, Majmaah University, Al Majmaah 11952, Saudi Arabia
2.
International Center for Interdisciplinary Research in Sciences, The University of Lahore, Lahore, Pakistan
3.
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
4.
Department of Mathematics, College of Science, Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
5.
Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia
6.
Department of Robotics, Hanyang University, Ansan 15588, Republic of Korea
7.
Department of Applied AI, Hanyang University, Ansan 15588 Republic of Korea
8.
School of Computing, Gachon University, Seongnam 13120, Republic of Korea

Received: 19 June 2026 Revised: 11 August 2026 Accepted: 21 August 2026 Published: 07 September 2026
MSC : 39A28, 39A30, 92D25

This paper investigates the dynamics of a predator-prey model with predator harvesting using a Mickens-type nonstandard finite difference (NSFD) scheme. The proposed discrete model preserves positivity and biological feasibility. The existence and local stability of the equilibrium points are analyzed, and conditions for transcritical and Neimark–Sacker bifurcations are derived. The direction and stability of the Neimark–Sacker bifurcation are determined using normal form theory. In contrast to the corresponding piecewise constant argument discretization, the proposed NSFD model excludes period-doubling and strong resonance bifurcations at the coexistence equilibrium. Decision tree, random forest, and support vector machine methods are also employed to classify the positive equilibrium and long-term dynamical behavior. Numerical simulations support the analytical results. The findings demonstrate that the proposed NSFD scheme provides a dynamically consistent framework for studying discrete predator-prey dynamics with harvesting.
- predator-prey model,
- harvesting effect,
- stability,
- bifurcation,
- Lyapunov functions,
- simulation,
- machine learning
Citation: Asifa Tassaddiq, Rizwan Ahmed, Rabab Alharbi, Dalal Khalid Almutairi, Ruhaila Md Kasmani, Youngmoon Lee, Jawad Khan. Dynamics, bifurcations, and machine learning-based analysis of a nonstandard discrete predator-prey model with predator harvesting[J]. AIMS Mathematics, 2026, 11(9): 28547-28581. doi: 10.3934/math.20261137

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Abstract

This paper investigates the dynamics of a predator-prey model with predator harvesting using a Mickens-type nonstandard finite difference (NSFD) scheme. The proposed discrete model preserves positivity and biological feasibility. The existence and local stability of the equilibrium points are analyzed, and conditions for transcritical and Neimark–Sacker bifurcations are derived. The direction and stability of the Neimark–Sacker bifurcation are determined using normal form theory. In contrast to the corresponding piecewise constant argument discretization, the proposed NSFD model excludes period-doubling and strong resonance bifurcations at the coexistence equilibrium. Decision tree, random forest, and support vector machine methods are also employed to classify the positive equilibrium and long-term dynamical behavior. Numerical simulations support the analytical results. The findings demonstrate that the proposed NSFD scheme provides a dynamically consistent framework for studying discrete predator-prey dynamics with harvesting.

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