Stationary Dynamics in a Stochastic Predator–Prey Model with a Fixed Wind-Intensity Index

Wind is an important abiotic factor that may influence predator–prey interactions. In this paper, we propose and analyze a stochastic predator–prey model in which the predator attack rate is described by a unimodal function of a fixed wind-intensity index. We establish the global existence, uniqueness, and positivity of solutions, together with stochastic ultimate boundedness, and derive a sufficient condition for the existence of a unique ergodic stationary distribution. A key analytical feature is that the Foster–Lyapunov recurrence argument is completed without quadratic predator self-limitation by exploiting the negative contribution generated by linear predator mortality. The resulting condition λ>0 incorporates effective predation, density dependence, wind modulation, predator mortality, and population-level environmental noise, and is a sufficient rather than necessary condition. Numerical parameter sweeps based on the complete expression for λ and simulations using a logarithmic Euler–Maruyama scheme illustrate parameter-specific changes in the sufficient-condition quantity and in the post-burn-in empirical population distributions.