A New Proof for the Existence of Topological Horseshoe in a Business Cycle Model

作者：Wu Wenjuan^*; Chen Zengqiang

来源：22nd Chinese Control and Decision Conference, 2010-05-26 to 2010-08-28.

• Chaos
• Topological Horseshoe
• Proof for the Existence
• Business Cycle Model

Complex chaotic dynamics is studies in the van der Pol oscillator model of business cycle forced by a sinusoidal function. The famous topological horseshoe theorem is applied to prove the existence of chaos from the mathematical viewpoint in this business cycle model. A rigorous proof for the existence of topological horseshoe is given. This technique combines the topological theory with the computer-assisted computations. A proper Poincare section is first chosen to obtain the corresponding Poincare map, which is proved to be semi-conjugate to the 2-shift map. This result implies that the business cycle model has positive topological entropy, and thus is definitely chaotic.

• 出版日期2010
• 单位南开大学