New Model for Prey–Predator Population Dynamics With Behaviorally Structured State Transition

This paper presents a prey–predator wildlife ecological model that explicitly categorizes predator populations into searching, hunting, and resting states within an SHRS‐type compartmental framework. It examines the influences of ecological factors such as prey availability and recovery on predator dynamics and establishes conditions for population persistence and extinction. The study identifies three equilibria and introduces a hunting predator reproduction number, , as a key threshold for predator survival. Parameters such as conversion efficiency, encounter rate, satiety rate, and handling time, together with numerical simulation analyses, confirm oscillatory dynamics influenced by predator mortality. The results highlight the critical balance of predator behaviors for the ecological stability of the wild animals in a park, indicating that high recovery rates with moderate attack levels favor coexistence. In contrast, excessive attack pressure can lead to instability and extinction. The model connects behavioral variations with ecological resilience, serving as a foundation for further research on complex ecological interactions. These findings suggest that managing predator populations and their behaviors is essential for maintaining biodiversity and ensuring the health of ecosystems. Future studies could explore additional factors such as environmental changes and human impact, which may further complicate these dynamics.