Unusual Liénard-type nonlinear oscillator

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 72, Issue 6, 2005, Pages

  Chandrasekar, V K ^a   Senthilvelan, M ^a   Lakshmanan, M ^a  

^a BHARATHIDASAN UNIVERSITY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

FLOW FUNCTION; LINEAR HARMONIC OSCILLATOR;

DYNAMICS; FUNCTIONS; HAMILTONIANS; STANDARDS;

OSCILLATORS (ELECTRONIC);

EID: 28844503236     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.066203     Document Type: Article

References (34)

1. A. H. Nayfeh and D. T. Mook, Nonlinear Oscillations (John Wiley, New York 1979).
2. J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (Springer-Verlag, New York, 1983).
3. M. Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction (J Wiley, New York, 1989).
4. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer-Verlag, New York, 2003).
5. M. Lakshmanan and S. Rajasekar, Nonlinear Dynamics: Integrability, Chaos and Patterns (Springer-Verlag, New York, 2003).
6. S. Chandrasekhar, An Introduction to the Study of Stellar Structure (Dover, New York, 1957);
7. J. M. Dixon and J. A. Tuszynski, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.41.4166 41, 4166 (1990).
8. F. M. Mahomed and P. G. L. Leach, Quaest. Math. 0379-9468 8, 241 (1985);
9. F. M. Mahomed and P. G. L. Leach, Quaest. Math. 0379-9468 12, 121 (1989);
10. P. G. L. Leach, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.526766 26, 2510 (1985);
11. P. G. L. Leach, M. R. Feix, and S. Bouquet, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.528096 29, 2563 (1988).
12. R. L. Devaney, Trans. Am. Math. Soc. TAMTAM 0002-9947 218, 89 (1976).
13. A. Politi, G. L. Oppo, and R. Badii, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.33.4055 33, 4055 (1986).
14. M. Sevryuk, Lect. Notes Math. LNMAA2 0075-8434 1211, (1986).
15. J. A. G. Roberts and G. R. W. Quispel, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(92)90163-T 216, 63 (1992).
16. J. S. W. Lamb, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/25/4/028 25, 925 (1992).
17. J. S. W. Lamb and J. A. G. Roberts, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00199-1 112, 1 (1998).
18. H. W. Broer, I. Hoveijn, and M. van Noort, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00201-7 112, 50 (1998).
19. H. Hanbmann, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00203-0 112, 81 (1998).
20. A. R. Champneys, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97) 00209-1 112, 158 (1998).
21. B. Liu, Trans. Am. Math. Soc. TAMTAM 0002-9947 10.1090/S0002-9947-99-01965-0 351, 515 (1999).
22. E. Lombardi, Lect. Notes Math. LNMAA2 0075-8434 1741, (2000).
23. S. Strogatz, Nonlinear Dynamics and Chaos (Westview, Cambridge, MA, 2000).
24. M. Prelle and M. Singer, Trans. Am. Math. Soc. TAMTAM 0002-9947 279, 215 (1983);
25. L. G. S. Duarte, S. E. S. Duarte, A. C. P. da Mota, and J. E. F. Skea, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/34/14/308 34, 3015 (2001).
26. V. K. Chandrasekar, M. Senthilvelan, and M. Lakshmanan, Proc. R. Soc. London PRLBA4 0962-8452 461, 2451 (2005).
27. A. J. Litchenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer-Verlag, New York, 1983).
28. J. L. McCauley, Chaos, Dynamics and Fractals: An Algorithmic Approach to Deterministic Chaos (Cambridge University Press, Cambridge, 1993).
29. P. G. Drazin, Nonlinear Systems (Cambridge University Press, Cambridge, 1992).
30. G. Nicolis, Introduction to Nonlinear Science (Cambridge University Press, Cambridge, 1995).
31. P. M. Mathews and M. Lakshmanan, Q. Appl. Math. QAMAAY 0033-569X 32, 215 (1974).
32. M. Lakshmanan and K. Eswaran, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/8/10/018 8, 1658 (1975).
33. P. W. Higgs, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/12/3/006 12, 309 (1979).
34. J. F. Carinena, M. F. Ranada, M. Santander, and M. Senthilvelan, Nonlinearity NONLE5 0951-7715 10.1088/0951-7715/17/5/019 17, 1941 (2004).