Abstract
On the basis of the method proposed in [1], the paper gives the method for finding the normal form of nonsemi-simple bifurcation problems. As an example, it analyses the normal form of a general nonlinear dynamical system with the nonsemi-simple double zero eigenvalues, and gives out the expression for the coefficients in the normal form by using those in the original system.
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References
Chen Yushu and Wu Zhiqiang, A new method for finding the normal form of a high dimensional dynamical system.
Wang Duo, An introduction to the normal form theory of ordinary differential equations,Advances in Mathematics,19, 1 (1990).
Chen Yushu,Bifurcation and Chaos Theory of Nonlinear Vibration Systems, Higher Education Press, Beijing (1993). (in Chinese)
Chen Yushu and Wu Zhiqiang, Normal form for multiple nonresonant Hopf bifurcation.
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Project supported by the National Natural Science Foundation and the Doctoral Programme from the State Education Commission of China
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Zhiqiang, W., Yushu, C. & Qinshen, B. Normal form of the nonsemi-simple bifurcation problem. Appl Math Mech 18, 349–354 (1997). https://doi.org/10.1007/BF02457549
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DOI: https://doi.org/10.1007/BF02457549