CODIMENSION-TWO BIFURCATIONS OF A TWO-DIMENSIONAL DISCRETE TIME LOTKA-VOLTERRA PREDATOR-PREY MODEL

In this paper, we investigate the codimension-two bifurcations of a two-dimensional discrete time predator-prey model, which is derived from a classical Lotka-Volterra type predator-prey system by the forward Euler scheme. It is shown that the model undergoes codimension-two bifurcations associated with 1:2, 1:3 and 1:4 resonances. The conditions for strong res-onance bifurcations are obtained by using the normal form method and the theory of approximation by a flow. Moreover, the bifurcation curves around 1:2 resonance are obtained and returned to the original parameters. Numerical simulations are provided to illustrate our theoretical results, and the model exhibits complex dynamical behaviors such as quasi-periodic orbits and the chaotic sets.