Dynamical Behaviors of a Discrete Two-Dimensional Competitive System Exactly Driven by the Large Centre

In this paper, a new discrete large-sub-center system is obtained by using the forward Euler scheme and the nonstandard discretization method for the corresponding continuous system. It is very surprised that all dynamic behaviors of the discrete system are exactly driven by the largecenter equation, for example, the stabilities, the bifurcations, the perioddoubling orbits, and the chaotic dynamics, etc. Especially, the global asymptotical stability, the existence of exact 2-periodic solutions, and the ip bifurcation theorem are induced by the large-center equation. Finally, those theoretical results are showed by some numerical simulations. To this end, the invariant set of the sub-center equation is also given.