一个三阶系统的Hopf分叉
Hopf Bifurcation in a Three-Dimensional System
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摘要: 本文利用Liapunov-Schmidt约化和奇点理论讨论了三阶系统-βy(1-kz),?=β[α(1-z)-ky2在全参数域上的Hopf分叉与退化的Hopf分叉,给出了周期解存在与稳定性条件.Abstract: In this paper,Liapunor-Schmidl reduction and singularity theory are employed to discuss Hopf and degenerate Hopf bifureations in global parametric region in a three-dimensional system , The conditions on existence and stability are given.
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[1] 李炳熙,《高维动力系统的周期轨道:理论与应用》,上海科技出版社(1984). [2] Golubitsky,M.and D.G.Schaeffer,Singularities and Groups in Bifurcation Theory,Vol.1. Springer-Verlag,New York(1985). [3] Golubitsky,M.and W.F.Langford,Classification and unfolding of degenerate Hopf bifureations,J.Diff.Eqs.,41(1981),375-415. [4] Golubitsky,M.and I.Stewart,Symmetry and Stability in Taylor-Couette flow,SIAM J,Math.Anal.,17(1986),249-288. [5] Chen,Y.S.and W.F.Langford,Subharmonic resonance in nonlinear Mathieu equations,天津大学学习班资料(1987). [6] Abragram,A.The Principle of Nuclear Magnetism,Oxford Univ.Press,New York(1961). [7] Sherman,S.,A third-order nonlinear system arising from a nuclear spin generator,Contr.Diff.Eqs.2(1963),197-227. -
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