Limit cycles and homoclinic orbits and their bifurcation of Bogdanov-Takens system

作者：Huang Cheng biao^*; Liu Jia

来源：Applied Mathematics and Mechanics, 2008, 29(9): 1195-1201.

DOI：10.1007/s10483-008-0908-6

• Bogdanov-Takens system
• limit cycle
• homoclinic orbit
• bifurcation diagrams
• analytical-expressions
• parameter incremental method

A quantitative analysis of limit cycles and homoclinic orbits, and the bifurcation curve for the Bogdanov-Takens system are discussed. The parameter incremental method for approximate analytical-expressions of these problems is given. These analytical-expressions of the limit cycle and homoclinic orbit are shown as the generalized harmonic functions by employing a time transformation. Curves of the parameters and the stability characteristic exponent of the limit cycle versus amplitude are drawn. Some of the limit cycles and homoclinic orbits phase portraits are plotted. The relationship curves of parameters mu and lambda with amplitude a and the bifurcation diagrams about the parameter are also given. The numerical accuracy of the calculation results is good.

• 出版日期2008-9
• 单位中山大学