Modeling predator–prey interactions under environmental and behavioural influences: a deterministic and stochastic approach

Predator‒prey dynamics do not rely entirely on biotic factors, but abiotic components significantly shape the system's behaviour, stability and long-term outcomes. In this study, we develop and analyze both deterministic and stochastic formulations of a tritrophic predator‒prey system that incorporates global warming, wind flow, herd behaviour, moonlight intensity and toxicant exposure. Global warming and wind flow are modeled as factors that decrease reproductive rates throughout the levels of the food chain, while herd geometry and moonlight account for adaptive behavioural responses in prey. Furthermore, the model includes the effects of toxicants impacting both intermediate and top predator species. For the deterministic model, we establish the boundedness and positivity of solutions, characterize equilibria and perform local and global stability analyses. A comprehensive bifurcation study revealed the occurrence of Hopf, transcritical, Bogdanov–Takens and generalized Hopf bifurcations, demonstrating rich dynamic behaviour under varying ecological pressures. The stochastic extension captures environmental fluctuations and provides insights into extinction probabilities, persistence conditions and noise-induced transitions. The sensitivity analysis highlights the ecological parameters that exert the greatest influence on system stability. Collectively, the results underscore how abiotic drivers, in conjunction with stochasticity, fundamentally alter predator‒prey interactions, thereby advancing the understanding of ecosystem responses under environmental change.