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参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉

DEGENERATE BIFURCATIONS OF CODIMENSION TWO IN NONLINEAR OSCILLATOR UNDER COMBINED PARAMETRIC AND FORCING EXCITATION

  • 摘要: 在本文里我们首先研究了具有Z_2-对称性的范式理论和退化向量场的普适开折理论。然后利用上述理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,从而解决了当解具有两个零特征值时解的稳定性问题。最后利用Melnikov方法求出了参数平面上的同宿分叉曲线,讨论了全局分叉的存在性。

     

    Abstract: In this paper, first we study normal form theory with Z2-symmetry and universal unfolding theory of the degenerate vector field. Then we use above mentioned theory to study degenerate bifurcations of codimension two in nonlinear oscillator under combined parame-tric and forcing excitation. Thereby stability problems with double zero eigenvalues can be solved. Finally the curves for homoclinic bifurcaron in parameter plane are given by using Melnikov's method and the existence of global bifurcation is discus...

     

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