A class of reversible quadratic systems with piecewise polynomial perturbations

Yanqin Xiong and Jianqiang Hu

Applied Mathematics and Computation, 2019, vol. 362, issue C, -

Abstract: This paper investigates a class of reversible quadratic systems perturbed inside piecewise polynomial differential systems of arbitrary degree n. All possible phase portraits of the reversible quadratic systems on the plane are obtained by analytic techniques. Then, we present the algebraic structure of its corresponding first-order Melnikov function, which can be used to study the limit cycle bifurcation problem. In this direction, we use it to investigate the Hopf bifurcation of the perturbed systems, and obtain an upper bound for the Hopf cyclicity. Meanwhile, we employ it to discuss the maximal number of limit cycles emerging from the periodic orbits around the origin for a special case and also provide its upper bound.

Keywords: Quadratic system; Melnikov function; Limit cycle (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319305065
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:362:y:2019:i:c:10

DOI: 10.1016/j.amc.2019.06.041

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().