《非线性Mathieu方程亚谐共振分叉理论》的一些推广
Some Extended Results of “Subharmonic Resonance Bifurcation Theory of Nonlinear Mathieu Equation”
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摘要: 在文[1]中,作者讨论了非线性Mathieu方程的亚谐共振分叉理论,得到的主要结果是,在参数α-β平面上,具有六种不同拓扑结构的分叉图.本文摧广了这一结果,指出:如果选取不同的芽来计算同样的分叉问题,则可以有十四种不同拓扑结构的分叉图.Abstract: The authors of [1] discussed the subharmonic resonance bifurcation theory of nonlinear Mathieu equation and obtained six bifurcation diagrams in (α,β )-plane. In this paper, we extended the results of[1] and pointed out that there may exist as many as fourteen bifurcation diagrams which are not topologically equivalent to each other.
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[1] 陈予恕,W.F.Langford,非线性马休方程的亚谐分叉解及欧拉动弯曲问题,力学学报,20,6(1988). [2] Golubitsky,M.and D.G.Schaeffer,Singularities and Groups in Bifurcation Theory,Vol.1,Springer-Verlag(1985). [3] 陈予恕、詹凯君,一类非线性参数振动系统的亚谐退化分叉理论(待发表). [4] 陈予恕、吴建国、金志胜.曲轴非线性参数扭振问题的分叉理论解,振动工程学报,1(i1987). -
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