On the number of limit cycles of a pendulum-like equation with two switching lines

Jihua Yang

Chaos, Solitons & Fractals, 2021, vol. 150, issue C

Abstract: This paper is devoted to study the limit cycle bifurcations of a pendulum equation x˙=y,y˙=−sinx under non-smooth perturbations of polynomials of cosx, sinx and y of degree n with switching lines x=0 and y=0. The upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained by expressing the corresponding first order Melnikov functions as several generating functions, some of which are complete elliptic integrals of the first and second kind.

Keywords: Pendulum equation; Generating function; Limit cycle; Melnikov function; Complete elliptic integral (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S096007792100446X
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:chsofr:v:150:y:2021:i:c:s096007792100446x

DOI: 10.1016/j.chaos.2021.111092

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().