LettersNo Access
BIFURCATIONS OF LIMIT CYCLES AND CENTER PROBLEM FOR A CLASS OF CUBIC NILPOTENT SYSTEM
https://doi.org/10.1142/S0218127410027210Cited by:20
Abstract
For a class of cubic nilpotent system, the formulae of the first eight quasi-Lyapunov constants are obtained. We show that the origin of this system is a center if and only if the first eight Lyapunov constants are zeros. Under a small perturbation, eight limit cycles can be created from the eight-order weakened focus.
This research was partially supported by the National Natural Science Foundation of China (10671179 and 10771196).
References
-
B. B. Amelikin , H. A. Lukashivich and A. P. Sadovski , Nonlinear Oscillations in Second Order Systems ( BGY Lenin. B. I. Press , Minsk , 1982 ) . Google Scholar - Int. J. Bifurcation and Chaos 15, 1253 (2005). Link, ISI, Google Scholar
- J. Math. Anal. Appl. 318, 271 (2006). Crossref, ISI, Google Scholar
-
A. M. Lyapunov , Stability of Motion, Mathematics in Science and Engineering 30 ( Academic Press , NY, London , 1966 ) . Google Scholar - J. Cent. South Univ. Technol. 30, 622 (1999). Google Scholar
- Int. J. Bifurcation and Chaos 19, 3791 (2009). Link, ISI, Google Scholar
- Int. J. Bifurcation and Chaos 19, 3087 (2009). Link, ISI, Google Scholar
- J. Diff. Eqs. (2009). Google Scholar
- Erg. Th. Dyn. Syst. 2, 241 (1982), DOI: 10.1017/S0143385700001553. Crossref, Google Scholar
- J. Diff. Eqs. 179, 479 (2002), DOI: 10.1006/jdeq.2001.4043. Crossref, ISI, Google Scholar
- Inst. Hautes Études Sci. Publ. Math. 43, 47 (1974), DOI: 10.1007/BF02684366. Crossref, Google Scholar
