BIFURCATION ANALYSIS OF A DELAYED PREDATOR-PREY MODEL WITH GLOBAL WARMING, WIND FLOW, HUNTING COOPERATION AND FEAR EFFECT

The impacts of abiotic factors on species are of great research significance. With the intensification of global warming, the interactions among species have become increasing complex. Meanwhile, species activities can exacerbate global warming, which in turn exerts multifaceted influences on the environmental carrying capacity of species, the predation processes, etc. Wind flow is an omnipresent component of the natural environment, and existing studies have indicated that wind speed exerts a notable influence on the predation efficiency of predators for their prey. Although abiotic factors are ubiquitous in nature, studies investigating their impacts on species interactions remain relatively scarce. In this paper, we propose a delayed predator-prey model that incorporates global warming and wind flow, as well as other factors including hunting cooperation and fear effect. First, we discuss the non-delayed model and prove the positivity and boundedness of the solutions. Then, the analysis of the related characteristic equations enables us to examine the existence and local stability of four equilibria. We also discuss the existence of bifurcations near different equilibria. For the model with time delay, the local stability of the positive equilibrium and the existence of Hopf bifurcation are addressed in our discussion. Furthermore, we analyze the direction of Hopf bifurcation and the stability of the periodic solutions by the center manifold theorem and normal form method. Finally, some numerical simulations are given to support our findings.