Bifurcation analysis in a Beddington–DeAngelis predator–prey model with habitat complexity and additional food effect

In this paper, we study a predator-prey model with a Beddington-DeAngelis functional response, where the effect of habitat complexity and additional food is proposed to jointly affect the dynamics of predator and prey. It is shown that the system can appear with a series of bifurcation phenomena, including Hopf bifurcation, saddle-node bifurcation, transcritical bifurcations at the x axis and the y axis, and a cusp type Bogdanov-Takens bifurcation of codimension two, and the system exhibits various dynamics, such as homoclinic orbits, multicoexistent periodic orbits, and a multicoexistent steady state. Several numerical examples are shown to verify our main results.