Vol. 7, No. 4 (2018): Regular Issue

In this paper, we investigate the dynamical complexities of a predator-prey model with Holling type IV functional response, which describes interaction between two populations of prey and predator. We perform a bifurcation analysis of this model analytically and numerically. Our bifurcation analysis indicates that the system exhibits numerous types of codimension one and two bifurcations including fold, subcritical and supercritical Hopf, cusp and Bogdanov-Takens. By numerical continuation method, we also compute several curves of equilibria and bifurcations. Further, by numerical simulations we reveal more complex dynamics of the model.