Anew Proof for the Existence of Topological Horseshoe in a 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 Poincaré section is first chosen to obtain the corresponding Poincaré 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.
Chaos Topological Horseshoe Proof for the Existence Business Cycle Model
Wenjuan Wu Zengqiang Chen
Department of Automation, Nankai University, Tianjin, 300071
国际会议
The 22nd China Control and Decision Conference(2010年中国控制与决策会议)
徐州
英文
3680-3685
2010-05-26（万方平台首次上网日期，不代表论文的发表时间）