Chaos controlling of extended nonlinear Liénard system based on the Melnikov theory

Applied Mathematics and Computation

Volumn 178, Issue 2, 2006, Pages 405-414

  Li, Ruihong ^a   Xu, Wei ^a   Li, Shuang ^a  

^a NORTHWESTERN POLYTECHNICAL UNIVERSITY   (China)

Author keywords

Bounded noise; Chaos control; Li nard system; Melnikov theory; Non feedback method; The top Lyapunov exponent

Indexed keywords

CHAOS THEORY; COMPUTATIONAL METHODS; CONTROL SYSTEM ANALYSIS; FUNCTION EVALUATION; LYAPUNOV METHODS;

BOUNDED NOISE; CHAOS CONTROL; LIÉNARD SYSTEM; MELNIKOV THEORY; NON-FEEDBACK METHOD; THE TOP LYAPUNOV EXPONENT;

NONLINEAR SYSTEMS;

EID: 33746228073     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.11.057     Document Type: Article

References (21)

1. Nayfeh A.H., and Mook D.T. Nonlinear Oscillations (1979), Wiley, New York
2. Lim C.W., and Wu B.S. A new analytical approach to the Duffing-harmonic oscillator. Phys. Lett. A 311 (2003) 365-373
3. Moukam Kakmeni F.M., Bowong S., Tchawoua C., and Kaptouom E. Strange attractors and chaos control in a Duffing-van der Pol oscillator with two external periodic forces. J. Sound Vib. 277 (2004) 783-799
4. Francisco Heitor I.P., Armando M.F., and Marcelo A.S. Chaos control in a nonlinear pendulum using a semi-continuous method. Chaos, Solitons Fract. 22 (2004) 653-668
5. Musielak D.E., Musielak Z.E., and Benner J.W. Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom. Chaos, Solitons Fract. 24 (2005) 907-922
6. Bishop S.R., Sofroniou A., and Shi P. Symmetry-breaking in the response of the parametrically excited pendulum model. Chaos, Solitons Fract. 25 (2005) 257-264
7. Attilio M. Modulated motion and infinite-period homoclinic bifurcation for parametrically excited Liénard systems. Int. J. Non-Linear Mech. 35 (2000) 239-262
8. Han M.A., Bi P., and Xiao D.M. Bifurcation of limit cycles and separatrix loops in singular Liénard systems. Chaos, Solitons Fract. 20 (2004) 529-546
9. Jitsuro S., and Yusuke A. Global asymptotic stability of nonautonomous systems of Liénard type. J. Math. Anal. Appl. 289 (2004) 673-690
10. Colin C., and James D. On the classification of Liénard systems with amplitude- independent periods. J. Differen. Equat. 200 (2004) 1-17
11. Ott E., Grebogi C., and Yorke J.A. Controlling chaos. Phys. Rev. Lett. 64 (1990) 1196-1199
12. Shinbrot T., Ott E., Grebogi C., and Yorke J.A. Using small perturbations to control chaos. Nature 363 (1993) 411-417
13. Shinbrot T., Ott E., Grebogi C., and Yorke J.A. Using chaos to direct trajectories. Phys. Rev. Lett. 65 (1990) 3215-3218
14. Lima R., and Pettini M. Suppression of chaos by resonant parametric perturbations. Phys. Rev. A 41 (1990) 726-733
15. Ramesh M., and Narayanan S. Chaos control by non-feedback methods in the presence of noise. Chaos, Solitons Fract. 10 (1990) 1473-1489
16. Braiman Y., and Goldhirsch I. Taming chaotic dynamics with weak periodic perturbations. Phys. Rev. Lett. 20 (1991) 2545-2548
17. Guckenheimer J., and Holmes P.J. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (1985), Springer-Verlag, New York
18. Wiggins S. Global Bifurcations and Chaos: Analytical Methods (1988), Springer, New York
19. Wolf A., Swift J.B., Swinney H.L., and Vastano J.A. Determining Lyapunov exponents from a time series. Physica D 16 (1985) 285-317
20. Liu W.Y., Zhu W.Q., and Huang Z.L. Effect of bounded noise on chaotic motion of Duffing oscillator under parametric excitation. Chaos, Solitons Fract. 12 (2001) 527-537
21. Arnold L. Random Dynamical Systems (1998), Springer, Berlin