On the limit cycles for continuous and discontinuous cubic differential systems
type: Item
instance of: scholarly article
title: On the limit cycles for continuous and discontinuous cubic differential systems
zbMATH Open document ID: 1378.34050
DOI: 10.1155/2016/4939780
author: Ziguo Jiang
published in: Discrete Dynamics in Nature and Society
publication date: 2017-11-13T00:00:00Z
review text: Summary: We study the number of limit cycles for the quadratic polynomial differential systems \(\dot{x} = - y + x^2\), \(\dot{y} = x + x y\) having an isochronous center with continuous and discontinuous cubic polynomial perturbations. Using the averaging theory of first order, we obtain that 3 limit cycles bifurcate from the periodic orbits of the isochronous center with continuous perturbations and at least 7 limit cycles bifurcate from the periodic orbits of the isochronous center with discontinuous perturbations. Moreover, this work shows that the discontinuous systems have at least 4 more limit cycles surrounding the origin than the continuous ones.
Mathematics Subject Classification ID: 34C07
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C29
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 6806278
zbMATH Keywords: isochronous center
zbMATH Keywords: averaging theory
zbMATH Keywords: continuous perturbations
zbMATH Keywords: discontinuous perturbations
Wikidata QID: Q59123530
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/4939780
OpenAlex ID: W2516634010
cites work: Q4715040
cites work: Averaging methods for finding periodic orbits via Brouwer degree.
cites work: On the birth of limit cycles for non-smooth dynamical systems
cites work: Limit cycles for a class of discontinuous planar quadratic differential system
cites work: Limit cycles for discontinuous quadratic differential systems with two zones
cites work: Limit cycles for a class of continuous and discontinuous cubic polynomial differential systems
cites work: Limit cycles bifurcate from centers of discontinuous quadratic systems
cites work: Limit cycles in discontinuous classical Liénard equations
cites work: Limit cycles for \(m\)-piecewise discontinuous polynomial Liénard differential equations
cites work: BIFURCATION OF LIMIT CYCLES IN PIECEWISE SMOOTH SYSTEMS VIA MELNIKOV FUNCTION
cites work: Center conditions in a switching Bautin system
cites work: Bifurcation of limit cycles from quadratic isochrones
cites work: Q3080073
description: scientific article; zbMATH DE number 6806278