Bounding the number of limit cycles for a polynomial Liénard system by using regular chains. (March 2017)

• Record Type: Journal Article
• Authors: Sun, Xianbo; Huang, Wentao
• Is Part Of: Journal of symbolic computation. Volume 79(2017)Part 2
• Page Start: 197
• Page End: 210
• Publication Date: 2017-03
• Subjects: Regular chain -- Limit cycle -- Liénard system -- Melnikov function; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2016.02.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, we study the bound of the number of limit cycles by Poincaré bifurcation for a Liénard system of type ( 4, 3 ) . An automatic algorithm is constructed based on the Chebyshev criteria and the tools of regular chain theory in polynomial algebra. We prove the system can bifurcate at most 6 limit cycles from the periodic annulus by this algorithm and at least 4 limit cycles by asymptotic expansions of the related Melnikov functions.