Stability of Equivariant Bifurcation Problems With Two Types of State Variables and Their Unfoldings in the Presence of Parameter Symmetry

CUI Deng-lan; LI Yang-cheng

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Article Navigation > Applied Mathematics and Mechanics > 2007 > 28(2): 209-215

CUI Deng-lan, LI Yang-cheng. Stability of Equivariant Bifurcation Problems With Two Types of State Variables and Their Unfoldings in the Presence of Parameter Symmetry[J]. Applied Mathematics and Mechanics, 2007, 28(2): 209-215.

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Stability of Equivariant Bifurcation Problems With Two Types of State Variables and Their Unfoldings in the Presence of Parameter Symmetry

CUI Deng-lan^1,2,
LI Yang-cheng¹

School of Mathematical Science and Computing Technology, Central South University, Changsha 410083, P. R. China;
College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, P. R. China

Received Date: 2005-06-08
Rev Recd Date: 2006-11-13
Publish Date: 2007-02-15

Abstract

Abstract

Based on the contact equivalent relation of smooth map-germs in singularity theory,the stability of equivariant bifurcation problems with two types of state variables and their unfoldings in the presence of parameters symmetry was discussed.Some basic results are obtained.Transversality condition was used to characterize the stability of equivariant bifurcation problems.
- equivariant bifurcation problem,
- unfolding,
- stability,
- infinitesimal stability

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References(7)

References

[1]	Gervais J J. Stability of unfoldings in the context of equivariant contact equivalence[J].Pacific J Math,1988,132(2):283-291.
[2]	Lari-Lavassani A, Lu Y C. On the stability of equivariant bifurcation problems and their unfoldings[J].Can Math Bull,1992,35(2):237-246. doi: 10.4153/CMB-1992-034-x
[3]	Lari-lavassani A, Lu Y C. Equivariant multiparameter bifurcations via singularity theory[J].J Dynamics Differential Equations,1993,5(2):189-218. doi: 10.1007/BF01053160
[4]	Golubitsky M, Stewart I, Schaeffer D C.Singularities and Groups in Bifurcation Theory[M].Vol 2. New York: Springer-Verlag, 1988.
[5]	Arnold V I, Gusein-Zade S M, Varchenko A N.Singularities of Differentiable Maps[M].Vol 1.Basel/Stuttgart：Birk Hauser,1985.
[6]	Damon J. The unfolaling and determinacy theorem for subgroups of A and K[R]. Vol 50,No 306.Memoirs AMS 306, Providence:AMS,1984:1-88.
[7]	CUI Deng-lan,LI Yang-cheng.The unfolding of equivariant bifurcation problems with two types of state variables in the presence of parameter symmetry[J].Acta Mathematica Sinica A,2006,22(5):1433-1440. doi: 10.1007/s10114-005-0712-4