Dynamic behavior of stochastic fast-slow fishery economic model with Allee effect

This article investigates a stochastic fast-slow fishery economic model with Allee effect. The fast-slow dynamic behavior of the deterministic system is discussed by using the theory of singular perturbation. Research shows that singular Hopf bifurcations will occur under the influence of strong Allee effect, while the dynamic behavior of the system will be more complex under the influence of weak Allee effect, resulting in relaxation oscillations. For the stochastic system, the existence of stationary distribution is discussed for both stochastic fast-slow system and system with time scale parameter as ordinary parameter. Then, the stochastic bifurcation behavior of the system is discussed, and it is found that stochastic-P bifurcation and stochastic-D bifurcation will occur. Finally, the correctness of the conclusion is verified through numerical simulation.