Primary resonant optimal control for nested homoclinic and heteroclinic bifurcations in single-dof nonlinear oscillators

Journal of Sound and Vibration

Volumn 289, Issue 1-2, 2006, Pages 229-244

  Cao, Hongjun ^a   Jiang, Yaozhen ^b   Shan, Yulin ^b  

^a BEIJING JIAOTONG UNIVERSITY   (China)

^b CHUXIONG NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); COSTS; NONLINEAR SYSTEMS; PENDULUMS;

CONTROL REGION; HETEROCLINIC BIFURCATIONS; NONLINEAR OSCILLATOR; SYSTEM DYNAMICS;

OSCILLATORS (MECHANICAL);

EID: 27344439118     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2005.02.027     Document Type: Article

References (15)

1. Y. Braiman, and I. Goldhirsch Taming chaotic dynamics with weak periodic perturbations Physical Review Letters 66 1991 2545 2548
2. G. Chen, and X. Dong From Chaos to Order: Methodologies, Perspectives, and Applications 1998 World Scientific Singapore
3. H. Cao, X. Chi, and G. Chen Suppressing or inducing chaos in a model of robot arms and mechanical manipulators Journal of Sound and Vibration 272 2004 705 724
4. H. Cao, X. Chi, and G. Chen Suppressing or inducing chaos by weak resonant excitations in an externally-forced Froude pendulum International Journal of Bifurcation and Chaos 14 3 2004 1115 1120
5. R. Chacón, F. Palmero, and F. Balibrea Taming chaos in a driven Josephson junction International Journal of Bifurcation and Chaos 7 2001 1897 1909
6. A. Lima, and M. Pettini Suppression of chaos by resonant parametric perturbations Physical Review A 41 1990 726 733
7. S. Rajasekar Controlling of chaos by weak periodic perturbations in Duffing-van der Pol oscillator Pramana 41 1993 295 309
8. J. Guckenheimer, and P. Holmes Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields 1983 Springer New York
9. S. Wiggins Introduction to Applied Nonlinear Dynamical Systems and Chaos 1990 Springer New York
10. S. Lenci, and G. Rega Optimal control of nonregular dynamics in a Duffing oscillator Nonlinear Dynamics 33 2003 71 86
11. S. Lenci, and G. Rega Optimal control of homoclinic bifurcation: theoretical treatment and practical reduction of safe basin erosion in the Helmholtz oscillator Journal of Vibration and Control 9 3 2003 281 316
12. S. Lenci, G. Rega, Heteroclinic bifurcations and optimal control in the nonlinear rocking dynamics of generic and slender rigid blocks, International Journal of Bifurcation and Chaos, in press.
13. M. Dabbs, and P. Smith Critical forcing for homoclinic and heteroclinic orbits of a rotating pendulum Journal of Sound and Vibration 189 2 1996 231 248
14. T. Parker, and L. Chua Practical Numerical Algorithms for Chaotic Systems 1989 Springer New York
15. S. Shaw, and S. Wiggins Chaotic dynamics of a whirling pendulum Physical D 31 1988 190 211