On the Problem of the Number of Bifurcation Solutions at Singular Point

Zhou Kun

Volume 18 Issue 10

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1997 > 18(10): 905-909

Zhou Kun. On the Problem of the Number of Bifurcation Solutions at Singular Point[J]. Applied Mathematics and Mechanics, 1997, 18(10): 905-909.

Citation:

Zhou Kun. On the Problem of the Number of Bifurcation Solutions at Singular Point[J]. Applied Mathematics and Mechanics, 1997, 18(10): 905-909.

Citation:

Zhou Kun. On the Problem of the Number of Bifurcation Solutions at Singular Point[J]. Applied Mathematics and Mechanics, 1997, 18(10): 905-909.

PDF( 329 KB)

On the Problem of the Number of Bifurcation Solutions at Singular Point

Zhou Kun

Department of Mechanics and Engineering Science, Peking University, Bejing 100871, P. R. China

Received Date: 1995-07-19
Rev Recd Date: 1997-01-01
Publish Date: 1997-10-15

Abstract

Abstract

In this paper,it is proved that the solutions of a nonlinear equation are isolated under Ihe condition that the singular points are isolated.It shows that there musl have and Only have finite solutions branching from bifurcation point.This is important.for the numerical analysis of bifurcation problems.
- homotopy,
- continuation method,
- bifurcation,
- isolated singularity

FullText(HTML)

References(4)

References

[1]	季海波、武际可、胡海昌,分叉问题的几何描述及其计算方法,中国科学(A),(9)(1991),947.
[2]	E.Allgower and K.Georg-Numerical Continuation Methods,Springer-Verlag(1990).
[3]	S.N.Chow and J.K.Hale,Methods of Bifurcation Theory,Springer-Verlag(1982).
[4]	武际可、苏先椒,《弹性系统的稳定性》,科学出版社(1994).

Relative Articles

[1]	TIAN Yaping, YANG Jianghui, WANG Ruibang. Parametric Solution Domain Structures for Bifurcation and Non-Meshing Dynamic Characteristics of Straight Bevel Gear Systems[J]. Applied Mathematics and Mechanics, 2023, 44(8): 965-976. doi: 10.21656/1000-0887.430330
[2]	ZHANG Jie, LI Xinying, YANG Zongkai, DA Hu. Effects of Time Delay on Bifurcation and Synchronization of Flux-Coupled and Chemically Coupled Neurons[J]. Applied Mathematics and Mechanics, 2022, 43(12): 1336-1346. doi: 10.21656/1000-0887.420381
[3]	PENG Rongrong. Analysis of Resonance and Bifurcation Characteristics of Some Duffing Systems With Quintic Nonlinear Restoring Forces[J]. Applied Mathematics and Mechanics, 2019, 40(10): 1122-1134. doi: 10.21656/1000-0887.390234
[4]	ZHANG Yanlong, WANG Li, SHI Jianfei. Bifurcation Evolution of Duffing Systems on 2-Parameter Planes[J]. Applied Mathematics and Mechanics, 2018, 39(3): 324-333. doi: 10.21656/1000-0887.380089
[5]	PIAO Jiang-min, HU Yu-da. Principal Resonance Bifurcation and Chaos of Rotating Annular Plates in Magnetic Fields[J]. Applied Mathematics and Mechanics, 2016, 37(11): 1181-1197. doi: 10.21656/1000-0887.370141
[6]	YI Zhuang-peng, ZHANG Yong, WANG Lian-hua. Nonlinear Dynamic Response and Bifurcation Analysis of the Elastically Constrained Shallow Arch[J]. Applied Mathematics and Mechanics, 2013, 34(11): 1182-1196. doi: 10.3879/j.issn.1000-0887.2013.11.008
[7]	LIU Yan-bin, CHEN Yu-shu, CAO Qing-jie. Chaos and Sub-Harmonic Resonance of Nonlinear System Without Small Parameters[J]. Applied Mathematics and Mechanics, 2011, 32(1): 1-10. doi: 10.3879/j.issn.1000-0887.2011.01.001
[8]	ZHONG Shun, CHEN Yu-shu. Bifurcation of Piecewise-Linear Nonlinear Vibration System of Vehicle Suspension[J]. Applied Mathematics and Mechanics, 2009, 30(6): 631-638. doi: 10.3879/j.issn.1000-0887.2009.06.001
[9]	WU Zhi-qiang, CHEN Yu-shu. Effects of Constant Excitation on Local Bifurcation[J]. Applied Mathematics and Mechanics, 2006, 27(2): 144-150.
[10]	WANG Xin-zhi, HAN Ming-jun, ZHAO Yan-ying, ZHAO Yong-gang. Nonlinear Dynamical Bifurcation and Chaotic Motion of a Shallow Conical Lattice Shell[J]. Applied Mathematics and Mechanics, 2006, 27(5): 586-590.
[11]	HU Yu-da, QIU Jia-jun, TA Na. Fundamental Resonance and Bifurcation of Large Generator End Winding When Its Clamping Plates Are Loose[J]. Applied Mathematics and Mechanics, 2005, 26(4): 465-473.
[12]	LIANG Jian-shu, CHEN Yu-shu, Andrew Y. T. Leung. Robust Control of Periodic Bifurcation Solutions[J]. Applied Mathematics and Mechanics, 2004, 25(3): 239-246.
[13]	QIU Ping, WANG Xin-zhi, YEH Kai-yuan. Bifurcation and Chaos of the Circular Plates on the Nonlinear Elastic Foundation[J]. Applied Mathematics and Mechanics, 2003, 24(8): 779-784.
[14]	WU Zhi-qiang, CHEN Yu-shu. Classification of Bifurcations for Nonlinear Dynamical Problems With Constraints[J]. Applied Mathematics and Mechanics, 2002, 23(5): 477-482.
[15]	MA Jun-hai, CHEN Yu-shu. Study for the Bifurcation Topological Structure and the Global Complicated Character of a Kind of Non-Linear Finance System(Ⅱ)[J]. Applied Mathematics and Mechanics, 2001, 22(12): 1236-1242.
[16]	MA Jun-hai, CHEN Yu-shu. Study for the Bifurcation Topological Structure and the Global Complicated Character of a Kind of Non-Linear Finance System(Ⅰ)[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1119-1128.
[17]	Cao Qingjie, Zhang Tiande, Li Jiuping. A Study of the Static and Global Bifurcations for Duffing Equation[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1309-1316.
[18]	Bi Qinsheng, Chen Yushu, Wu Zhiqiang. Bifurcation in a Nonlinear Duffing System with Multi-Frequency External Periodic Forces[J]. Applied Mathematics and Mechanics, 1998, 19(2): 113-120.
[19]	Liao Shijun, . Homotopy Analysis Method: a New Analytic Method for Nonlinear Problems[J]. Applied Mathematics and Mechanics, 1998, 19(10): 885-890.
[20]	He Lu-wu, Cheng Chang-jun. The Buckled States of Rectangular Plates[J]. Applied Mathematics and Mechanics, 1992, 13(5): 401-406.