Abstract:
This talk is concerning a joint work with Shigui Ruan and Yilei Tang about the versal unfolding of a predator–prey system with ratio-dependent functional response near a degenerate equilibrium in order to obtain all possible phase portraits for its perturbations. We first construct the
unfolding and prove its versality and degeneracy of codimension 2. Then we discuss all its possible bifurcations, including transcritical bifurcation, Hopf bifurcation, and heteroclinic bifurcation, give conditions of parameters for the appearance of closed orbits and heteroclinic loops, and describe the bifurcation curves. Phase portraits for all possible cases are presented.
Tea Time: 3:30PM R707