| THEORY AND COMPUTATION OF SECONDARY BIFURCATIONS NEAR A DOUBLE EIGENVALUE |
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| 作者姓名： | 吴柏生 李荣华 |
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| 作者单位： | Department of Mathematics，Jilin University，Changchun 130023，PRC.，Department of Mathematics，Jilin University，Changchun 130023，PRC. |
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| 基金项目： | Supported by the National Education Foundation of China |
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| 摘 要： | This paper deals with secondary bifurcations near a double eigenvalue of a nonlinear equation with two parameters. Utilizing symmetries (or more generally, equivariances ) and introducing two new parameters, we give some extended systems so that the double singular points, secondary bifurcation points and initial secondary branches respectively become their regular solutions. The methods in this paper not only give more general conditions of secondary bifurcation but also avoid the adjacent singularities of existing extended systems for computing the simple bifurcation points on non-trivial solution branches A numerical example is presented, showing the effectiveness of our methods.
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THEORY AND COMPUTATION OF SECONDARY BIFURCATIONS NEAR A DOUBLE EIGENVALUE |
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| Wu Bai-sheng.THEORY AND COMPUTATION OF SECONDARY BIFURCATIONS NEAR A DOUBLE EIGENVALUE[J].Numerical Mathematics A Journal of Chinese Universities English Series,1992(1). |
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| Authors: | Wu Bai-sheng |
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| Institution: | Wu Bai-sheng Department of Mathematics,Jilin University,Changchun 130023,PRC. LiRong-hua Department of Mathematics,Jilin University,Changchun 130023,PRC. |
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| Abstract: | This paper deals with secondary bifurcations near a double eigenvalue of a nonlinear equation with two parameters. Utilizing symmetries (or more generally, equivariances ) and introducing two new parameters, we give some extended systems so that the double singular points, secondary bifurcation points and initial secondary branches respectively become their regular solutions. The methods in this paper not only give more general conditions of secondary bifurcation but also avoid the adjacent singularities of existing extended systems for computing the simple bifurcation points on non-trivial solution branches A numerical example is presented, showing the effectiveness of our methods. |
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| Keywords: | Double eigenvalue symmetries singularities extended systems secondary bifurcations |
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