Numerical Research of a Economic Model Based on Topological Horseshoes Theory

Recently, research for complex dynamical behavior of financial or economic systems by means of nonlinear theory and method has become a new hot spot. In this paper, we firstly optimize the parameter of system using Lyapunov Exponent Method, and then transform the model to the Poincaré map by choosing proper Poincaré plane and find two different types of topological horseshoe with expanding in one direction in the phase space of corresponding the Poincare map. Not only it finds strictly that the topological horseshoe exists widely in the economic model, but also verifies strictly the chaos in math to reveal the dynamical principle of chaos.