Dynamics, Bifurcations, and Machine Learning-Based Analysis of a Nonstandard Discrete Predator-Prey Model with Predator Harvesting

초록

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.

키워드