Approximating the amplitude and form of limit cycles in the weakly nonlinear regime of Liénard systems

Chaos, Solitons and Fractals

Volumn 34, Issue 4, 2007, Pages 1307-1317

  Lopez J L ^a   Lopez Ruiz R ^b  

^a PUBLIC UNIVERSITY OF NAVARRE   (Spain)

^b UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); FUNCTIONS;

CONTINUOUS FUNCTIONS; LIMIT CYCLES;

NONLINEAR SYSTEMS;

EID: 34247174332     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.04.031     Document Type: Article

References (21)

1. Winfree A. The timing of biological clocks (1986), Scientific American Library, W.H. Freeman Co, San Francisco (CA)
2. Andronov A.A., Vitt A.A., and Khaikin S.E. Theory of oscillators (1989), Dover, New York
3. Ilyashenko Y. Centennial history of Hilbert's 16th problem. Bull Amer Math Soc 39 (2002) 301-354
4. Li J. Hilbert's 16th problem and bifurcations of planar polynomial vector fields. Int J Bifurc Chaos 13 (2003) 47-106
5. Ecalle J., Martinet J., Mousse R., and Ramis J.P. Non-accumulation des cycles limits I-II. C R Acad Sci Paris I 304 (1987) 375-431
6. Ilyashenko Y. Finitess theorems for limit cycles. Russ Math Surveys 45 (1990) 129-203
7. Ye Y. Theory of limit cycles. Trans Math Monographs vol. 66 (1986), American Mathematical Society, Boston
8. Li J., and Huang Q. Bifurcations of limit cycles forming compound eyes in the cubic system. Chin Ann Math B 8 (1987) 391-403
9. Zhang T., Han M., Zan H., and Meng X. Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations. Chaos, Solitons & Fractals 22 (2004) 1127-1138
10. 6-equivariant planar vector field of degree 5. Sci China Ser A 45 (2002) 817-826
11. Odani K. The limit cycle of the van der Pol equation is not algebraic. J Differen Equat 115 (1995) 146-152
12. López-Ruiz R., and Pomeau Y. Transition between two oscillation modes. Phys Rev E 55 (1997) R3820-R3823
13. Lins A., de Melo W., and Pugh C.C. On Liénard's equation. Lectures notes in math vol. 597 (1977), Springer, New York 355
14. 2 i + 1 is two. Differen Equat 11 (1975) 301-302
15. López J.L., and López-Ruiz R. The limit cycles of Liénard equations in the strongly nonlinear regime. Chaos, Solitons & Fractals 11 (2000) 747-756
16. Giacomini H., and Neukirch S. Number of limit cycles of the Liénard equation. Phys Rev E 56 (1997) 3809-3813
17. Jordan D.W., and Smith P. Nonlinear ordinary differential equations (1977), Oxford University Press, Oxford
18. Padín M.S., Robbio F.I., Moiola J.L., and Chen G. On limit cycle approximations in the van der Pol oscillator. Chaos, Solitons & Fractals 23 (2005) 207-220
19. López-Ruiz R., and López J.L. Bifurcation curves of limit cycles in some Liénard systems. Int J Bifurcat Chaos 10 (2000) 971-980
20. López J.L., and López-Ruiz R. Number and amplitude of limit cycles emerging from topologically equivalent perturbed centers. Chaos, Solitons & Fractals 17 (2003) 135-143
21. Van Horssen W.T. A perturbation method based on integrating factors. SIAM J Appl Math 59 (1999) 1427-1443