Dynamical Behavior Analysis of Fixed Points of Investment Competition Model

First, based on Logistic map, a duopoly investing model with discrete formula is constructed for the homogeneous firms. Then, the long-time evolution processes of the model are analyzed including the stability of fixed points, bifurcations and chaotic behaviors. Moreover, the economic implication characterized the dynamics behaviors are indicated. The results show that in some extent of parameter, the final results of the model are stable points, and in other parameter extent the final results are quasi-periodic motion or chaotic attractor. It's interesting that with the increase of parameter chaos induced by double periodic bifurcation replaced by stable equilibrium. Finally, numerical simulations are presented to verify the results.