Citation: | 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. |
[1] |
Krylov N,Bogoliubov N.Les methods de la mecarique nonlinear[J].Monographie.Chaire de la Phys and Math of Academic Science.U K,1934,8:44—51.
|
[2] |
CHEN Yu-shu,Langford W F.The subharmonic bifurcation solution of nonlinear Mathieu's equation and Euler dynamically bucking problem[J].Acta Mech Sinica,1988,20(4):522—532.
|
[3] |
Yu P,Huseyin K.Parametrically exited nonlinear systems:a comparison of certain methods[J].Int J Non-Linear Mechanics,1998,33(6):967—978. doi: 10.1016/S0020-7462(97)00061-9
|
[4] |
Chow S Y,Hale J K.Methods of Bifurcation Theory[M].New York:Springer,1982.
|
[5] |
Golubisky M,Schaeffer D G.Singularities and Groups in Bifurcan'on Theory(Vol.[STHZ]. 1[STBZ]. )[M].New York:Springer,1985.
|
[6] |
Bogoliubov N,Mitropolsky Y A.Asymptotic Methods in the Theory of Nonlinear Oscillations[M].New York:Gordon & Breach,1961.
|
[7] |
Nayfeh A H,Mook D T.Nonlinear Osci Uations[M].New York:Wiley,1979.
|
[8] |
Abed E H,Wang H O,Chen R C.Stabilization of period doubling bifurcation and implications for control of chaos[J].Physica D,1994,70(1):154—164. doi: 10.1016/0167-2789(94)90062-0
|
[9] |
Wang H O,Abed E H.Bifurcation control of a chaotic system[J].Automatica,1995,31(9):1213—1226. doi: 10.1016/0005-1098(94)00146-A
|
[10] |
Kang W.Bifurcation and normal form of nonlinear control systems—Parts Ⅰand Ⅱ[J].SIAM J Contr Optim,1998.36(1):193—232.
|
[11] |
Chen G,Dong X.From Chaos to Order:Methodologies,Perspectives and Applications[M].Singapore:World Scientific Pub Co,1998.
|
[12] |
Abed E H.Bifurcation-theoretic issues in the control of voltage collapse[A].In:Chow J H,Kokotovic P V,Thomas R J Eds.Proc IMA Workshop on Systems and Control Theory for Power Sys[C].New York:Springer,1995,1—21.
|
[13] |
Chen G,Lu J,Yap K C.Controlling Hopf bifurcation[A].In:Ueta T,Chen G Eds.Proc Int Symp Circ Sys[C].3.USA:Monterey, C A,1998,693—642.
|
[14] |
Basso M,Evangelisti A,Genesio R,et al.On bifurcation control in time delay feedback systems[J].Int J Bifur Chaos,1998,8(4):713—721. doi: 10.1142/S0218127498000504
|
[15] |
Chen G.Controlling Chaos and Bifurcation in Engineering Systems[M].Boca Raton,FL:CRC Press,1999.
|
[16] |
Chen G,Moiola J L,Wang H O.Bifurcation control:theories,methods and applications[J].Int J Bifur Chaos,2000,10(3):511—548.
|
[17] |
CHEN Yu-shu,Leung Andrew Y T.Bifurcation and Chaos in Engineering[M].London:Springer,1998.
|
[18] |
陈予恕,杨彩霞,吴志强,等.具有平方、立方非线性项的耦合动力学系统1:2内共振分岔[J].应用数学和力学,2001,22(8):817—824.
|
[19] |
LI Xin-ye,CHEN Yu-shu,WU Zhi-qiang,et al.Bifurcation of nonlinear normal modes of M-DOF systems with internal resonance[J].Acta Mechanica Sinica,2002,34(3):104—407.
|
[20] |
Sundararajan P,Noah S.Dynamics of forced nonlinear systems using shooting arc length continuation method[J].ASME J Vib Acoustics,1995,119(1):9—20.
|
[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] | 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 |
[8] | WU Zhi-qiang, CHEN Yu-shu. Effects of Constant Excitation on Local Bifurcation[J]. Applied Mathematics and Mechanics, 2006, 27(2): 144-150. |
[9] | 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. |
[10] | 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. |
[11] | 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. |
[12] | 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. |
[13] | CHEN Yu-shu, DING Qian. C-L Method and Its Application to Engineering Nonlinear Dynamical Problems[J]. Applied Mathematics and Mechanics, 2001, 22(2): 127-134. |
[14] | 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. |
[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(Ⅰ)[J]. Applied Mathematics and Mechanics, 2001, 22(11): 1119-1128. |
[16] | Zhao Yucheng, Yuan Shuqing, Xiao Zhonghui, Xu Qingyu. The Fractional Dimension Identification Method of Critical Bifurcated Parameters of Bearing-Rotor System[J]. Applied Mathematics and Mechanics, 2000, 21(2): 126-130. |
[17] | Zhang Jiazhong, Hua Jun, Xu Qingyu. A Method of Following the Unstable Path Between Two Saddle-Node Bifurcation Points in Nonlinear Dynamic System[J]. Applied Mathematics and Mechanics, 1999, 20(12): 1281-1285. |
[18] | 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. |
[19] | 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. |
[20] | Zhou Kun. On the Problem of the Number of Bifurcation Solutions at Singular Point[J]. Applied Mathematics and Mechanics, 1997, 18(10): 905-909. |