An Improved Recursive Formula for Computing Normal Forms of Multi-dimensional Dynamical Systems


	Journal of Applied Sciences
	Year: 2013 \| Volume: 13 \| Issue: 15 \| Page No.: 2924-2928 DOI: 10.3923/jas.2013.2924.2928

An Improved Recursive Formula for Computing Normal Forms of Multi-dimensional Dynamical Systems

Lei Guo, Qunhong Li and Zigen Song

Abstract: In this study, an improved explicit recursive formula of normal forms under nonlinear near-identity transformations is firstly introduced and the associated proof is also given out. Compared with traditional method, the improved method can get the specific expression of the higher order terms of dynamical systems after nonlinear transformations. So the normal forms of the original dynamical systems can be obtained by a series of nonlinear transformations but without changing its topology structure, also by solving a series of algebra equations with the aid of computing software Maple, not only the coefficients of the jth order normal form and the associated nonlinear transformations but also higher (>j) order terms of the original equations can be obtained. The application of the improved method will greatly simplify the computation during the research of dynamical systems.

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How to cite this article:

Lei Guo, Qunhong Li and Zigen Song , 2013. An Improved Recursive Formula for Computing Normal Forms of Multi-dimensional Dynamical Systems. Journal of Applied Sciences, 13: 2924-2928.

DOI: 10.3923/jas.2013.2924.2928

URL: https://scialert.net/abstract/?doi=jas.2013.2924.2928

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