Strange attractors and chaos control in a Duffing-Van der Pol oscillator with two external periodic forces

Journal of Sound and Vibration

Volumn 277, Issue 4-5, 2004, Pages 783-799

  Kakmeni, F M Moukam ^a   Bowong, S ^b   Tchawoua, C ^a   Kaptouom, E ^a  

^a Univ de Yaounde I   (France)

^b INRIA   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; FEEDBACK; NONLINEAR SYSTEMS; OSCILLATIONS; OSCILLATORS (MECHANICAL); PROBLEM SOLVING;

CHAOS CONTROL; EXTERNAL FORCES; PERIODIC FORCES;

ACOUSTICS;

EID: 4544341749     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsv.2003.09.051     Document Type: Article

References (18)

1. Guckenheimer J., Holmes P. Nonlinear Oscillation and Bifurcation of Vector Fields. 1993;Springer, New York.
2. Atlee Jackson E. Perspectives of Nonlinear Dynamics. 1991;Cambridge University Press, New York.
3. Lakshmanan M., Murali K. Chaos in Nonlinear Oscillators: Controlling and Synchronization. 1996;World Scientific, Singapore.
4. Kozlov A.K., Sushchik M.M., Molkov Ya.I., Kuznetsov A.S. Bistable phase synchronization and chaos in system of coupled Van der Pol-Duffing oscillators. International Journal of Bifurcation and Chaos. 9:1999;2271-2277.
5. Szemplińska-Stupnicka W., Rudowski J. Neimark bifurcation, almost-periodicity and chaos in the forced van der Pol-Duffing system in the neighbourhood of the principal resonance. Physics Letters A. 192:1994;201-206.
6. Venkalesam A., Lakshmanan M. Bifurcation and chaos in the double well Duffing-van der Pol oscillator. numerical and analytical studies Physical Review E. 56:1997;6321-6330.
7. van der Pol B. Forced oscillations in a circuit with nonlinear resistance (receptance with reactive triode). London, Edinburgh, and Dublin Philosophical Magazine. 7:1927;65-80.
8. Ge Z.M., Lin T.N. Chaos, chaos control and synchronization of a gyrostat system. Journal of Sound and Vibration. 251:2002;519-542.
9. Yagasaki K. Chaotic motions near homoclinic manifold and resonant toris in quasiperiodic perturbations of planar Hamiltonian systems. Physica D. 69:1993;269-322.
10. Yagasaki K. Homoclinic motion and chaos in the quasiperiodically forced Van der Pol-Duffing oscillator with single well potential. Proceedings of the Royal Society of London A. 445:1994;597-617.
11. Ott E., Grebogi C., Yorke J. Controlling chaos. Physica Review E. 64:1990;1196-1199.
12. W.J. Freeman, The physiology of perception, Scientific American (1991) 78-85.
13. A. Iggidr, G. Sallet, Exponential stabilization of nonlinear systems by an estimated state feedback, Proceedings of the Second European Control Conference EEC'93, Groningen, The Netherlands, 1993, pp. 2015-2018.
14. Teel A., Praly L. Tool for semiglobal stabilization by partial state and output feedback. SIAM Journal of Control and Optimization. 33:1991;424-431.
15. Moukam F.K., Bowong S., Tchawoua C. Exponential stabilization of two nonlinearly coupled oscillators by an estimated state feedback. Physica Scripta. 66:2002;7-15.
16. R. Femat, J. Alvarez-Ramirez, B. Castillo-Toledo, J. Gonzalez, On robust chaos suppression in a class of nondriven oscillators: application to the Chua's circuit, IEEE Circuits and Systems I: Fundamental Theory and Applications 46 1150-1152.
17. Chua L.O., Yang T., Zhong G.Q., Wu C.W. Adaptive synchronization of Chua oscillations. International Journal of Bifurcation and Chaos. 6:1996.
18. Sussman H.J., Kokotovic P.V. The peaking phenomenon and the global stabilization of nonlinear systems. IEEE Transactions on Automatic Control. 36:1991;461-472.