常数激励对局部分岔的影响

基金项目: 国家自然科学基金资助项目(10472078;10102014);天津市自然科学基金资助项目(043103611;013604711)

Effects of Constant Excitation on Local Bifurcation

摘要: 用奇异性理论讨论了常数激励对1/2内共振系统周期解局部分岔的影响．研究表明，常数激励项能否产生影响关键取决于低频振子中是否存在某些非线性项．常数激励，一方面起主分岔参数的作用，另一方面，与系统中某些非线性项的系数一起确定分岔解基本类型、影响开折参数．在非退化条件下，可不考虑三次非线性项的影响．
- 内共振 /
- 常数激励 /
- 分岔
Abstract: The effects of the constant excitation on the local bifurcation of the periodic solutions in the 1:2 internal resonant systems were analyzed based on the singularity theory. It is shown that the constant excitation make influence only when there exist nonlinear terms, in the oscillator with lower frequency. Besides acting as main bifurcation parameter, the constant excitation, together with coefficients of some nonlinear terms, may change the values of unfolding parameters and the type of the bifurcation. Under the non-degenerate cases, the effect of the third order terms can be neglected.
- internal resonance /
- constant excitation /
- bifurcation

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