Bifurcation analysis of a predator-prey system with generalised Holling type III functional response

We consider a generalised Gause predator-prey system with a generalised Holling response function of type III: p(x) - mx(2)/ax(2) + bx + 1. We study the cases where b is positive or negative. We make a complete study of the bifurcation of the singular points including: the Hopf bifurcation of codimensions 1 and 2, the Bogdanov - Takens bifurcation of codimensions 2 and 3. Numerical simulations are given to calculate the homoclinic orbit of the system. Based on the results obtained, a bifurcation diagram is conjectured and a biological interpretation is given.