Analysis on an Oscillator with Delayed Feedback Near Double Hopf Bifurcations

American Society of Mechanical Engineers, Design Engineering Division (Publication) DE

Volumn 111, Issue , 2001, Pages 117-128

  Yu, P ^a   Yuan, Y ^a  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); CLOSED LOOP CONTROL SYSTEMS; EQUATIONS OF MOTION; FEEDBACK CONTROL; MATHEMATICAL MODELS; OSCILLATORS (ELECTRONIC);

CHAOTIC MOTIONS;

NONLINEAR CONTROL SYSTEMS;

EID: 0242552906     PISSN: 15214613     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (10)

1. A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations, John Wiley & Sons, New York, 1979.
2. J. M. T. Thompson and H. B. Stewart, Nonlinear Dynamics And Chaos: Geometrical Methods For Engineers And Scientists, Wiley, New York, 1986.
3. H. Goldstein, Classical Mechanics, Addison-Wesley, Reading, MA, 1980.
4. F. C. Moon, Chaotic and Fractal Dynamics, A Eiley-Interscience Publication, New York, 1992.
5. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1993.
6. J. Bélair and S. A. Campbell, Stability and bifurcations of equilibria in multiple-delayed differential equation, SIAM J. Appl. Math. 54 (1994) 1402-1424.
7. V. Wulf and N. J. Ford, Numerical Hopf bifurcation for a class delay differential equations, J. Comput. & Appl. Math. 115 (2000) 601-616.
8. D. V. R. Reddy, A. Sen and G. L. Johnston, Dynamics of a limit cycle oscillator under time delayed linear and nonlinear feedbacks, Physica D 144 (2000) 335-357.
9. J. Hale and S. Lunel, Introduction Functional Differential Equations, Springer-Verlag, New York, 1993.
10. P. Yu, Symbolic computation of normal forms for resonant double Hopf bifurcations using multiple time scales, J. Sound & Vib. (2001, in press).