Hopf Bifurcation Analysis in a Reaction-Diffusion-Advection Model with Strong Allee Effect and Delay

This paper investigates a delayed reaction-diffusion-advection population model that incorporates delay and strong Allee effect. Firstly, the effect of the advection rate on the stability of constant steady state within the model is examined. Analysis indicates that under the given conditions, larger advection rate can stabilize the constant steady state. Then, the existence of Hopf bifurcations is studied by adopting delay as the varying parameter. Besides, the normal form in the vicinity of the Hopf singularity on the center manifold is calculated by adopting a weighted inner product. Simulations are conducted to validate the theoretical findings. Research shows that under certain conditions, there exists a sequence of bifurcation singularities in the system.