Hopf bifurcation analysis in a reaction-diffusion-advection model with strong Allee effect and delay

This paper investigates a delayed population model incorporating advection and strong Allee effect. First, we prove the well-posedness of the solutions in the model. The effect of the advection rate on the dynamics of the population is examined. Analysis indicates that under the given conditions, a larger advection rate can stabilize the equilibrium of the model. Second, by adopting delay as the varying parameter, the Hopf bifurcation of the model is studied. Third, the normal form in the vicinity of the Hopf bifurcation singularity is calculated by adopting a weighted inner product. The reliability of the conclusion is then verified by means of the numerical simulations. Research shows that under specific conditions, there exists a sequence of Hopf bifurcation singularities in the system.