A Discrete Predator–Prey Model With Neem-Dependent Growth Suppression: Stability and Bifurcation Analysis for Guava Pest Control

In this paper, we have developed a discrete-time predator–prey system to discuss the theoretical basis of guava-pest management, incorporating the novel neem-leaf treatment k, the key bifurcation parameter, logistic prey growth, and the Holling Type-II functional response. The continuous counterpart has been discretized by using the forward Euler scheme to align with pulsed, seasonal management operations. We concluded that the system observes the complex dynamics, including the flip and Neimark–Sacker bifurcation, which demonstrate the shift of a stable regime to periodic, oscillatory behavior and then to chaos. The detailed study of bifurcation and stability concluded that neem intensity k plays the key role of bifurcation parameter, and we have developed a parameter threshold at which the system either loses stability or can be recovered and finally delay the chaos. Our theoretical results have been justified by the numerical examples along with the bifurcation diagrams and maximum Lyapunov exponent that demonstrate how the interplay between treatment intensity k and application frequency δ interact to mitigate the long-term behavior. In spite of this work being purely theoretical, we have concluded that a novel mathematical framework in the context of bifurcation theory and utilizing the biologically meaningful control parameters plays a significant role in the ecological modeling. The findings in this paper provide a structure for intervention methodologies and build a foundation for future empirical validation, parameter estimation, and use in different crop-pest systems within integrated pest management (IPM).