Complex dynamic behaviour of an economic cycle model

作者：Zhao, Ming^*; Li, Cuiping

来源：Journal of Difference Equations and Applications, 2016, 22(12): 1777-1790.

DOI：10.1080/10236198.2016.1244267

• Economic cycle model
• stability
• bifurcation
• Marotto's chaos
• feedback control

In this paper, we investigate the dynamics of a nonlinear economic cycle model. The necessary and sufficient conditions are given to guarantee the existence and stability of the fixed point. It is also shown that the system undergoes a Neimark-Sacker bifurcation by using center manifold theorem and bifurcation theory. Furthermore, Marotto's chaos is proved when certain conditions are satisfied. Numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviour, such as the period-10, -16, -20 orbits, attracting invariant cycles, quasi-periodic orbits, 10-coexisting chaotic attractors, and boundary crisis. Specifically, we have stabilized the chaotic orbits at an unstable fixed point using the feedback control method.

• 出版日期2016
• 单位北京航空航天大学