Amplitude control of limit cycle in van der Pol system

International Journal of Bifurcation and Chaos

Volumn 16, Issue 2, 2006, Pages 487-495

  Tang, Jiashi ^a   Chen, Zili ^b  

^a HUNAN UNIVERSITY   (China)

^b Central South Forestry University   (China)

Author keywords

Amplitude; Control; Hopf bifurcation; Limit cycle; Van der Pol oscillator

Indexed keywords

AMPLITUDE MODULATION; BIFURCATION (MATHEMATICS); FEEDBACK CONTROL; NUMERICAL ANALYSIS; OSCILLATORS (ELECTRONIC); SYSTEMS ANALYSIS;

AMPLITUDE CONTROL; FEEDBACK CONTROLLERS; LIMIT CYCLES; VAN DER POL SYSTEM;

NONLINEAR SYSTEMS;

EID: 33645658932     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127406014952     Document Type: Review

References (9)

1. Chen, G., Moiola, J. L. & Wang, H. O. [2000] "Bifurcation control: Theories, methods, and applications," Int. J. Bifurcation and Chaos 10, 511-548.
2. Lopez-Ruiz, R. [2004] "Symmetry induced oscillations in four-dimensional models deriving from the van der Pol equation," Chaos Solit. Fract. 21, 55-61.
3. Maccari, A. [2003] "Vibration control for the primary resonance of the van der Pol oscillator by a time delay state feedback," Int. J. Nion-Lin. Mech. 38, 123-131.
4. Mickens, R. E. & Gumel, A. B. [2002] "Numerical study of a non-standard finite-difference scheme for the van der Pol equation," J. Sound Vibr. 250, 955-963.
5. Mickens, R. E. [2003] "Fractional van der Pol equations," J. Sound Vibr. 259, 457-460.
6. Moiola, J. L., Berns, D. W. & Chen, G. [1997] "Feedback control of limit cycle amplitudes," Proc. IEEE Conf. Decis. Contr., San Diego, CA, pp. 1479-1485.
7. Nayfeh, A. H. & Mook, D. T. [1978] Nonlinear Oscillations, John Wiley, NY.
8. Nayfeh, A. H., Harb, A. M. & Chin, C. M. [1996] "Bifurcations in a power system model," Int. J. Bifurcation and Chaos 6, 497-512.
9. Tang, J. S., Fu, W. B. & Li, K. A. [2002] "Bifurcations of a parametrically excited oscillator with strong nonlinearity," Chinese Phys. 11, 1004-1007.