Abstract
In this paper, a class of quintic systems is investigated. The first 13 focal values are computed with the aid of MATHEMATICA. Then the necessary conditions of integrability and linearizability are obtained and the sufficiency of every condition is proved. Meanwhile, bifurcation of limit cycles is discussed, 13 limit cycles can be bifurcated from the origin. As far as the number of limit cycles enclosing an isolated singular point is concerned, this is so far the best result for elementary singular points.
Funder
National Natural Science Foundation of China
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference24 articles.
1. On the number of limit cycles appearing with variation of the coefficients from an equilibrium state of the type of a focus or a center;Bautin;Mat. Sb. (N.S.),1952
2. A Cubic System with Eight Small-Amplitude Limit Cycles
3. Symbolic computation of limit cycles associated with Hilbert’s 16th problem
4. AN APPLICATION OF REGULAR CHAIN THEORY TO THE STUDY OF LIMIT CYCLES
5. A cubic differential system with nine limit cycles;Lloyd;J. Appl. Anal. Comput.,2012