Ten Limit Cycles in a Quintic Lyapunov System
نویسنده
چکیده
In this paper, center conditions and bifurcation of limit cycles at the nilpotent critical point in a class of quintic polynomial differential system are investigated. With the help of computer algebra system MATHEMATICA, the first 10 quasi Lyapunov constants are deduced. As a result, sufficient and necessary conditions in order to have a center are obtained. The fact that there exist 10 small amplitude limit cycles created from the three order nilpotent critical point is also proved. Henceforth we give a lower bound of cyclicity of three-order nilpotent critical point for quintic Lyapunov systems. At last, we give an system which could bifurcate 10 limit circles. Keywords—Three-order nilpotent critical point, Center-focus problem, Bifurcation of limit cycles, Quasi-Lyapunov constant.
منابع مشابه
Local bifurcation of limit cycles and center problem for a class of quintic nilpotent systems
* Correspondence: [email protected] School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, Henan, P. R. China Full list of author information is available at the end of the article Abstract For a class of fifth degree nilpotent system, the shortened expressions of the first eight quasi-Lyapunov constants are presented. It is shown that the orig...
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