Dynamical behaviors of a generalist predator–prey system with Allee and wind effects in deterministic or stochastic environment

In deterministic or stochastic environment, a generalist predator–prey system with the additive Allee effect and wind flow is explored by incorporating the Beverton–Holt type functional response to describe the influence of additional food on the growth of predators. First of all, in deterministic surroundings, we focus on positivity and boundedness of solutions, existence and stability of equilibrium points. Meanwhile, the occurrences of Hopf and transcritical bifurcations are analyzed by using the Hopf bifurcation theorem and Sotomayor’s theorem, respectively. It is worth mentioning that, in stochastic environment, the stochastic average theory is applied to simplify the stochastic system. The stability and stochastic bifurcations (P-bifurcation and D-bifurcation) are examined in accordance with Lyapunov exponent, invariant measure and singular boundary theory. Last but not least, our theoretical findings are consistent with numerical fruits.