Complex dynamics of a Leslie–Gower model with supplementary food and habitat selection: Effects of stochastic and impulsive disturbances

In natural ecosystems, population dynamics are invariably influenced by two fundamental types of environmental perturbations: (1) continuous stochastic fluctuations arising from random environmental variations, and (2) discrete, pulse-like disturbances caused by both natural events and human activities. These impulsive effects typically occur at specific time points with relatively short durations but significant ecological impacts. To accurately capture these complex interactions, we develop and analyze an impulsive stochastic Leslie–Gower predator–prey model that incorporates three key ecological features: a Crowley–Martin functional response, supplementary food availability, and habitat selection behavior. Our analytical investigation proceeds through several key stages: (i) demonstrate the existence of the unique globally positive solution; (ii) investigate the existence of periodic solutions and derive conditions for stochastic persistence; (iii) analyze the global attractivity of solutions and population extinction thresholds; (iv) conduct comprehensive simulations to verify all theoretical predictions. This systematic approach provides a rigorous mathematical foundation for understanding how stochasticity, impulsive effects, and ecological factors interact to shape predator–prey dynamics in realistic environmental conditions.