Stability and bifurcation analysis of a predator-prey system with feedback-controlled odour and wind-driven decay

Chemical communication is a fundamental component of predator-prey interactions, significantly influencing prey vigilance and predator hunting efficiency. Despite its ecological importance, prevailing mathematical models commonly treat odour as a static or externally imposed parameter, thereby overlooking its inherently dynamic nature and the reciprocal feedback between chemical cues and population dynamics. In this study, we present a novel three-dimensional model incorporating odour concentration as a dynamic variable, directly influenced by predator density and species interactions. Our model captures odour production, its natural decay through environmental processes such as wind-mediated dissipation, and the resultant non-consumptive effects on prey, including stress-induced reductions and alterations in vigilance behaviour. We rigorously analyse the qualitative dynamics of the model. Specifically, we perform stability analyses of all biologically feasible equilibria and detect various bifurcation phenomena, such as transcritical and Hopf bifurcations. The dynamics of the system are also examined across various two-parametric spaces. Extensive numerical simulations corroborate our theoretical findings and facilitate a detailed investigation of parameter influences. Furthermore, we compute the normalized forward sensitivity index to quantify the relative impact of model parameters.