Quasi-periodic solutions and sub-harmonic bifurcation of Duffing's equations with quasi-periodic perturbation

Acta Mathematicae Applicatae Sinica

Volumn 15, Issue 4, 1999, Pages 374-384

  Xu, Pengcheng ^a   Jing, Zhujun ^a  

^a INSTITUTE OF GEOLOGY AND GEOPHYSICS   (China)

Author keywords

Duffing's equation; Quasi periodic perturbation; Quasi periodic solutions; Sub harmonic bifurcation curves

Indexed keywords

EID: 4243126536     PISSN: 01689673     EISSN: 16183932     Source Type: Journal    
DOI: 10.1007/bf02684038     Document Type: Article

References (15)

1. S. Wiggens. Introduction to Applied Nonlinear Dynamical System and Chaos. Springer-Verlag, New York, 1990
2. S. Wiggens. Global Bifurcations and Chaos. Springer-Verlag, New York, 1988
3. S. Wiggens. Chaotic Transport in Dynamical Systems. Springer-Verlag, New York, 1992
4. J. Guckenheimer, P. Holmos. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. World Publishing Crop., 1983
5. J. J. Stoker. Nonlinear Vibrations in Mechanical and Electrical Systems. Interscience Publisher Inc., 1992
6. S. Wiggens, P. Holmes. Homoclinic Orbits in Slowly Varying Oscillators. SIAM J. Math. Anal., 1987, 18: 612-629
7. K. Yagasaki. Second-order Averaging and Chaos in Quasiperiodically Forced Weakly Nonlinear Oscillators. Physica D, 1990, 44: 445-458
8. K. Yagasaki. Chaos Dynamics of Quasiperiodically Forced Beam. Trans. ASMA. J. Appl. Mech., 1992, 59: 161-167
9. K. Yagasaki. Chaos in Pendulum with Feedback Control. Nonlinear Dynamics, 1994, 6: 125-142
10. K. Yagasaki. Bifurcations and Chaos in a Quasi-periodically Forced Beam: Theory, Simulation and Experiment. J. Sound and Vibration, 1995, 183: 1-31
11. K. Ide, S. Wiggens. The Bifurcation to Homoclinic Tori in the Quasiperiodically Forced Duffing's Oscillator. Physica D, 1989, 34: 169-192
12. Wanda Szemplintial-Stupnicka, Jerzy Rudowski. Steady State in the Twin-well Potential Oscillator: Computer Simulation and Approximate Analysis. Chaos, 1993, 3: 105-112
13. Jing Zhujun, Wang Pengyuan. Analysis of Duffing's Equation with Periodic Force and Without Damping: Combination Oscillation and Subharmonic Solutions and Chaotic Solution - A Study of Biomathematical Model of Aeurysm of Willis. Ann. Diff. Eqs., 1989, 5: 297-303
14. J. Moser. Combination Tones for Duffing's Equation. Comm. Pure Appl. Math., 1965, 18: 176-181
15. B. liu, J. You. KAM Tori for Quasi-periodic Forced Differential Equations. Proceeding's of the Conference on Qualitative Theory of Ordinary Equations, 1993, 23-27