Dynamical analysis of two coupled parametrically excited van der Pol oscillators

International Journal of Non-Linear Mechanics

Volumn 39, Issue 1, 2004, Pages 33-54

  Bi, Qinsheng ^a  

^a JIANGSU UNIVERSITY   (China)

Author keywords

Chaos; The second Poincare map; Van der Pol oscillator

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS;

SYMMETRIC CHAOTIC ATTRACTORS;

OSCILLATORS (ELECTRONIC);

EID: 0037475219     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7462(02)00126-9     Document Type: Article

References (16)

1. Rand R.H., Holmes P.J. Bifurcation of periodic motions into weakly coupled van der Pol oscillators. Internat. J. Non-linear Mech. 15:1980;387-399.
2. Storti D.W., Rand R.H. Dynamics of two strongly coupled van der Pol oscillators. Internat. J. Non-linear Mech. 17:1982;143-152.
3. Kouda A., Mori S. Mode analysis of a system of mutually coupled van der Pol oscillators with coupling delay. Internat. J. Non-linear Mech. 17:1982;267-276.
4. Chakraborty T., Rand R.H. The transition from phase locking to drift in a system of two weakly coupled van der Pol oscillators. Internat. J. Non-linear Mech. 23:1988;369-376.
5. Dieci L., Lorenz R., Russell R.D. Numerical calculations of invariant tori for two weakly coupled van der Pol oscillators. SIAM, J. Sci. Statist. Comput. 12:1990;607-647.
6. Gilsinn D.E. Constructing invariant tori for two weakly coupled van der Pol oscillators. Nonlinear Dyn. 4:1993;289-308.
7. Gilsim D.E. Construction Galerkin's approximations of invariant tori using MACSYMA. Nonlinear Dyn. 8:1995;269-305.
8. Ge T., Leung A.Y.T. Construction of invariant torus using Toeplitz Jacobian Matrices/fast Flourier transform approach. Nonlinear Dyn. 15:1998;283-305.
9. Maccari A. Approximation solution of a class of non-linear oscillators in resonance with periodic excitation. Nonlinear Dyn. 15:1998;329-343.
10. Maccari A. A model system for the behavior of two non-linear coupled oscillators. J. Sound Vib. 215:1998;313-330.
11. Maccari A. Nonlinear oscillations with multiple resonant or non-resonant forcing terms. Internat. J. Non-linear Mech. 34:1999;27-34.
12. Maccari A. Modulated motion and infinite-period bifurcation for two non-linearly coupled and parametrically excited van der Pol oscillators. Internat. J. Non-linear Mech. 36:2001;335-347.
13. Bi Qinsheng, Yu Pei Computation of normal forms of differential equations associated with non-zero eigenvalues. Internat. J. Bifurc. Chaos. 8:1998;2279-2319.
14. Chow S.N., Li C.Z., Wang D. Normal Forms and Bifurcations of Planar Vector Fields. 1994;Cambridge University Press, Cambridge.
15. Bi Qinsheng, Dai Hui-hui Analysis of non-linear dynamics and bifurcation of a shallow arch subjected to periodic excitation with internal resonance. J. Sound Vib. 233:2000;557-571.
16. Bi Qinsheng, Yu Pei Double Hopf bifurcations and chaos of a non-linear vibration system. Nonlinear Dyn. 19:1999;294-317.