Complex dynamics in pendulum equation with parametric and external excitations II

International Journal of Bifurcation and Chaos

Volumn 16, Issue 10, 2006, Pages 3053-3078

  Jing, Zhujun ^a,b   Yang, Jianping ^a,c  

^a CHINESE ACADEMY OF SCIENCES   (China)

^b HUNAN NORMAL UNIVERSITY   (China)

^c UNIVERSITY OF CHINESE ACADEMY OF SCIENCES   (China)

Author keywords

Averaging method; Bifurcations; Chaos; Melnikov's method; Pendulum equation; Quasi periodicity

Indexed keywords

CHAOS THEORY; COMPUTER SIMULATION; LYAPUNOV METHODS; NUMERICAL ANALYSIS; PENDULUMS; PERTURBATION TECHNIQUES;

AVERAGING METHOD; COMPLEX DYNAMICS; MELNIKOV'S METHOD; PENDULUM EQUATION; QUASI PERIODIC PERTURBATION;

WAVE EFFECTS;

EID: 33845525059     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127406016653     Document Type: Article

References (24)

1. Anischchenko, V. S., Astakhov, V. V., Neiman, A. B., Vadivasova, T. E. & Schimansky-Geier, L. [2002] Nonlinear Dynamics of Chaotic and Stochastic Systems (Springer).
2. Arnold, V. I. [1992] Ordinary Differential Equations (Springer-Verlag).
3. Chen, G. [1998] From Chaos to Order (World Scientific, Singapore).
4. Chua, L. O., Desoe, C. A. & Kuch, E. S. [1987] Linear and Nonlinear Circuits (McGraw-Hill, NY).
5. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, NY).
6. Hilborn, R. C. [2000] Chaos and Nonlinear Dynamics, 2nd edition (Oxford University Press).
7. Holmes, P. J. [1980] "Averaging and chaotic motion in forced oscillations," SIAM J. Appl. Math. 38, 65-80.
8. Jing, Z. J. & Yang, J. P. [2006] "Complex dynamics in pendulum equation with parametric and external excitations I," Int. J. Bifurcation and Chaos 16, 2887-2902.
9. Jordan, D. W. & Smith, P. [1987] Nonlinear Ordinary Differential Equations, 2nd edition (Clarendon Press).
10. Lakshmanan, M. & Murali, K. [1996] Chaos in Nonlinear Oscillators: Controlling and Synchronization (World Scientific, Singapore).
11. Landa, P. S. [2001] Regular and Chaotic Oscillations (Springer).
12. Melnikov, V. K. [1963] "On the stability of the center for time periodic perturbations," Trans. Moscow. Math. Soc. 12, 1-57.
13. Minorsky, N. [1962] Nonlinear Oscillations (D. Van Nostrand Company, INC).
14. Moon, F. C. [1992] Chaotic and Fractal Dynamics (John Wiley, Inc).
15. Nayfeh, A. H. & Mook, D. T. [1979] Nonlinear Oscillations (John Wiley, NY).
16. Nayfeh, A. H. & Balachandran, B. [1994] Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods (Wiley-Interscience).
17. Ott, E. [1993] Chaos in Dynamical Systems (Cambridge University Press).
18. Sanders, J. A. & Verhulst, F. [1985] Averaging Methods in Nonlinear Dynamical Systems (Springer-Verlag, NY).
19. Sastry, S. [1999] Nonlinear System: Analysis, Stability, and Control (Springer).
20. Thompson, J. M. & Stewart, H. B. [2002] Nonlinear Dynamics and Chaos, 2nd edition (John Wiley).
21. Wiggins, S. [1988] Global Bifurcation and Chaos: Analytical Methods (Springer-Verlag).
22. Wiggins, S. [1990] Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer-Verlag).
23. Yagasaki, K. [1990] "Second-order averaging and chaos in quasiperodically forced weakly nonlinear oscillator," Physica D 44, 445-458.
24. Yagasaki, K. [1996] "Second-order averaging and Melnikov analysis for forced nonlinear oscillators," J. Sound Vibr. 190, 587-609.