|
[1]
|
Bruno, A.D. (1989) Local Methods in Nonlinear Differential Equations. Springer-Verlag, Berlin, Heidelberg.
http://dx.doi.org/10.1007/978-3-642-61314-2 [Google Scholar] [CrossRef]
|
|
[2]
|
Starzhinskii, V.M. (1980) Applied Methods in the Theory of Nonlinear Oscillations. Mir Publishers, Moscow.
|
|
[3]
|
Bruno, A.D. and Edneral, V.F. (2006) Normal Forms and Integrability of ODES Systems. Programming and Computer Software, 32, 139-144. http://dx.doi.org/10.1134/S0361768806030042 [Google Scholar] [CrossRef]
|
|
[4]
|
Poincaré, H. (1879) Sur les Propriétés des Fonctions Définies par des Equations aux Différences Partielles Thèse Inaugural. Gauthier-Villars.
|
|
[5]
|
Zhang, W. and Yao, M.H. (2006) Multi-Pulse Orbits and Chaotic Dynamics in Motion of Parametrically Excited Viscoelastic Moving Belt. Chaos, Solitons and Fractals, 28, 42-66. http://dx.doi.org/10.1016/j.chaos.2005.05.005 [Google Scholar] [CrossRef]
|
|
[6]
|
Zhang W., Wang, F.X. and Yao, M.H. (2005) Global Bifurcation and Chaotic Dynamics in Nonlinear Nonplanar Oscillations of a Parametrically Excited Cantilever Beam. Nonlinear Dynamics, 40, 251-279.
http://dx.doi.org/10.1007/s11071-005-6435-3 [Google Scholar] [CrossRef]
|
|
[7]
|
Manuel, F.P., Manuel, P.M., Javier, G.C. and José, A.B. (2014) Stability and Chaotic Behavior of a PID Controlled Inverted Pendulum Subjected to a Harmonic Base Excitations by Using the Normal Form Theory. Applied Mathematics and Computation, 232, 698-718. http://dx.doi.org/10.1016/j.amc.2014.01.102 [Google Scholar] [CrossRef]
|
|
[8]
|
Zhang, W. and Li, J. (2001) Global Analysis for a Nonlinear Vibration Absorber with Fast and Slow Modes. International Journal of Bifurcation and Chaos, 11, 2179-2194. http://dx.doi.org/10.1142/S0218127401003334 [Google Scholar] [CrossRef]
|
|
[9]
|
曾京, 徐涛. 客车系统非线性横向稳定性的分叉研究[J]. 西南交通大学学报, 1994, 29(3): 316-322.
|
|
[10]
|
周稻详. 种群生态模型的分叉与稳定性研究[D]: [硕士学位论文]. 重庆: 重庆大学, 2013.
|
|
[11]
|
张波, 曾京, 董浩. 非线性轮对陀螺系统的稳定性及分叉研究. 振动: 测试与诊断, 2015, 35(5): 955-960.
|
|
[12]
|
Erika, R., Eric, A. and Gerardo, G. (2016) Stability and Bifurcation Analysis of a SIR Model with Saturated Incidence Rate and Saturated Treatment. Mathematics and Computers Simulation, 121, 109-132.
http://dx.doi.org/10.1016/j.matcom.2015.09.005 [Google Scholar] [CrossRef]
|
|
[13]
|
Chen, G. and Della Dora, J. (2000) Further Reductions of Normal Forms for Dynamical Systems. Journal of Differential Equations, 166, 79-106. http://dx.doi.org/10.1006/jdeq.2000.3783 [Google Scholar] [CrossRef]
|
|
[14]
|
Hao, Y.X., Zhang, W. and Yang, J. (2011) Analysis on Nonlinear Oscillations of a Cantilever FGM Rectangular Plate Based on Third-Order Plate Theory and Asymptotic Perturbation Method. Composites Part B: Engineering, 42, 402- 413. http://dx.doi.org/10.1016/j.compositesb.2010.12.010 [Google Scholar] [CrossRef]
|
|
[15]
|
Zhang, W., Song, C.Z. and Ye, M. (2006) Further Studies on Nonlinear Oscillations and Chaos of a Rectangular Symmetric Cross-By Laminated Plate under Parametric Excitation. International Journal of Bifurcation and Chaos, 16, 325-347. http://dx.doi.org/10.1142/S0218127406014836 [Google Scholar] [CrossRef]
|
|
[16]
|
Zhang, W., Hao, Y.X., Guo, X.Y. and Chen, L.H. (2012) Complicated Nonlinear Response of a Simply Supported FGM Rectangular Plate under Combined Parametric and External Excitations. Mecanica, 47, 985-1014.
http://dx.doi.org/10.1007/s11012-011-9491-4 [Google Scholar] [CrossRef]
|
|
[17]
|
Ogata, K. (1970) Modern Control Engineering. Prentice-Hall, Englewood Cliffs.
|