Dynamics and modulated chaos for two coupled oscillators

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 14, Issue 1, 2004, Pages 337-346

  Qinsheng, B I ^a  

^a JIANGSU UNIVERSITY   (China)

Author keywords

Modulated chaos; Poincar map; Van der pol oscillator

Indexed keywords

BIFURCATION (MATHEMATICS); DEGREES OF FREEDOM (MECHANICS); ELECTRIC EXCITATION; NATURAL FREQUENCIES; OSCILLATIONS; OSCILLATORS (ELECTRONIC);

COUPLED OSCILLATORS; MODULATED CHAOS; PHASE LOCKING;

CHAOS THEORY;

EID: 6344290617     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127404009041     Document Type: Article

References (13)

1. Bi, Q. & Dai, H. H. [2000] "Analysis of nonlinear dynamics and bifurcation of a shallow arch subjected to periodic excitation with internal resonance," J. Sound Vibr. 233, 557-571.
2. Chakraborty, T. & Rand, R. H. [1988] "The transition from phase locking to drift in a system of two weakly coupled van der Pol oscillators," Int. J. Nonlin. Mech. 23, 369-376.
3. Dieci, L., Lorenz, R. & Russell, R. D. [1990] "Numerical calculations of invariant tori for two weakly coupled van der Pol oscillators," SIAM, J. Sci. Stat. Comput. 12, 607-647.
4. Ge, T. & Leung, A. Y. T. [1998] "Construction of invariant torus using Toeplitz Jacobian matrices/fast Flourier transform approach," Nonlin. Dyn. 15, 283-305.
5. Gilsim, D. E. [1995] "Construction Galerkin's approximations of invariant tori using MACSYMA," Nonlin. Dyn. 8, 269-305.
6. Kouda, A. & Mori, S. [1982] "Mode analysis of a system of mutually coupled van der Pol oscillators with coupling delay," Int. J. Nonlin. Mech. 17, 267-276.
7. Maccari, A. [1998] "Approximation solution of a class of nonlinear oscillators in resonance with periodic excitation," Nonlin. Dyn. 15, 329-343.
8. Maccari, A. [2001] "Modulated motion and infiniteperiod bifurcation for two non-linearly coupled and parametrically excited van der Pol oscillators," Int. J. Nonlin. Mech. 36, 335-347.
9. Rand, R. H. & Holmes, P. J. [1980] "Bifurcation of periodic motions into weakly coupled van der Pol oscillators," Int. J. Nonlin. Mech. 15, 387-399.
10. Storti, D. W. & Rand, R. H. [1982] "Dynamics of two strongly coupled van der Pol oscillators," Int. J. Nonlin. Mech. 17, 143-152.
11. Tien, W. M., Namachchivaya, N. S. & Bajaj, A. K. [1994a] "Non-linear dynamics of a shallow arch under periodic excitation-I. 1:2 internal resonance," Int. J. Nonlin. Mech. 29, 349-366.
12. Tien, W. M., Namachchivaya, N. S. & Malhotra, N. [1994b] "Non-linear dynamics of a shallow arch under periodic excitation-II. 1:1 internal resonance," Int. J. Nonlin. Mech. 29, 367-386.
13. Wiggins, S. [1988] Global Bifurcation and Chaos (Springer, NY).