Limit Cycles and Integrability of a Class of Quintic System

Yanli Tang, Dongmei Zhang and Feng Li ()
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Yanli Tang: Center for International Education, Philippine Christian University, Manila 1004, Philippines
Dongmei Zhang: School of Mathematics and Statistics, Linyi University, Linyi 276005, China
Feng Li: School of Mathematics and Statistics, Linyi University, Linyi 276005, China

Mathematics, 2022, vol. 10, issue 16, 1-11

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.

Keywords: focal value; limit cycle; center; isochronous center (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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