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	SIMPLEST NORMAL FORMS FOR PLANAR SYSTEMS ON EQUILIBRIUM MANIFOLDS
	Lin, Mu ; Tang, Yun ; Chen, Guanrong ; Shi, Yuming
	2010-10-12 ; 2010-10-12
关键词	Planar system equilibrium manifold simplest normal form GENERIC HOPF-BIFURCATION UNIQUE NORMAL FORMS VECTOR-FIELDS PARAMETERS LINES SINGULARITIES REDUCTION Mathematics, Interdisciplinary Applications Multidisciplinary Sciences
中文摘要	Equilibrium manifold is a manifold that consists of equilibrium points. Planar systems with one-dimensional equilibrium manifolds are considered in this paper. First, for such planar systems, a unified equation with the horizontal axis as the equilibrium curve is formulated. Then, according to the corresponding linearized systems, different cases are discussed: For the nondegenerate case, the simplest normal form of a system with simplified Bogdanov-Takens singularities is obtained; for the general first-order degenerative case, the simplest normal forms are completely characterized; finally, for the general higher-order degenerative case, deduction of the simplest normal form is illustrated.
语种	英语 ; 英语
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD ; SINGAPORE ; 5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/81318]
专题	清华大学
推荐引用方式 GB/T 7714	Lin, Mu,Tang, Yun,Chen, Guanrong,et al. SIMPLEST NORMAL FORMS FOR PLANAR SYSTEMS ON EQUILIBRIUM MANIFOLDS[J],2010, 2010.
APA	Lin, Mu,Tang, Yun,Chen, Guanrong,&Shi, Yuming.(2010).SIMPLEST NORMAL FORMS FOR PLANAR SYSTEMS ON EQUILIBRIUM MANIFOLDS..
MLA	Lin, Mu,et al."SIMPLEST NORMAL FORMS FOR PLANAR SYSTEMS ON EQUILIBRIUM MANIFOLDS".(2010).

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