Limit cycles and invariant curves in a class of switching systems with degree four
type: Item
instance of: scholarly article
title: Limit cycles and invariant curves in a class of switching systems with degree four
zbMATH Open document ID: 1425.34048
DOI: 10.1155/2018/4716047
author: Xinli Li
author: Bing-Hong Wang
author: Huijie Yang
published in: Journal of Function Spaces
publication date: 2019-01-11T00:00:00Z
review text: Consider a special planar polynomial system of degree four having \(y=0\) as a line of discontinuity and the conic \(x^2+ cy^2=1\), \(c\in\mathbb{R}\), as an invariant curve. The authors study the bifurcation of limit cycles from the origin with \(c\) as bifurcation parameter under the condition that the first eight Lyapunov constants vanish.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 7000100
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/4716047
OpenAlex ID: W2901269258
cites work: Q5496558
cites work: Twelve limit cycles around a singular point in a planar cubic-degree polynomial system
cites work: Bifurcation of limit cycles and isochronous centers for a quartic system
cites work: Theory of rotated equations and applications to a population model
cites work: Q3868118
cites work: Q3871220
cites work: Small limit cycles bifurcating from fine focus points in cubic order \(Z_{2}\)-equivariant vector fields
cites work: A cubic system with twelve small amplitude limit cycles
cites work: A STUDY ON THE EXISTENCE OF LIMIT CYCLES OF A PLANAR SYSTEM WITH THIRD-DEGREE POLYNOMIALS
cites work: Small limit cycles bifurcating from fine focus points in quartic order \(Z_{3}\)-equivariant vector fields
cites work: Bifurcations of the limit cycles in a \(z_3\)-equivariant quartic planar vector field
cites work: A cubic system with thirteen limit cycles
cites work: \(Z_{2}\)-equivariant cubic system which yields 13 limit cycles
cites work: EXISTENCE CONDITIONS OF THIRTEEN LIMIT CYCLES IN A CUBIC SYSTEM
cites work: An Improvement on the Number of Limit Cycles Bifurcating from a Nondegenerate Center of Homogeneous Polynomial Systems
cites work: Q3828315
cites work: Q5669600
cites work: Quadratic systems having a parabola as an integral curve
cites work: Q3148585
cites work: Solution of the problem of the centre for a cubic differential system with three invariant straight lines
cites work: Coexistence of limit cycles and invariant algebraic curves for a Kukles system
cites work: A cubic system with an invariant triangle surrounding at least one limit cycle.
cites work: Limit cycles of a cubic Kolmogorov system
cites work: A cubic Kolmogorov system with six limit cycles
cites work: Cubic Kolmogorov system with invariant straight lines.
cites work: Reversibility in polynomial systems of ODE's
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: Dynamics and bifurcations of non-smooth mechanical systems
cites work: Generalized Hopf bifurcation for planar Filippov systems continuous at the origin
cites work: Limit cycles bifurcate from centers of discontinuous quadratic systems
cites work: Center conditions in a switching Bautin system
cites work: Center and isochronous center conditions for switching systems associated with elementary singular points
cites work: Bifurcation of periodic orbits by perturbing high-dimensional piecewise smooth integrable systems
cites work: Bifurcation theory for finitely smooth planar autonomous differential systems
cites work: Coexistence of small and large amplitude limit cycles of polynomial differential systems of degree four
Wikidata QID: Q128898711
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description: scientific article; zbMATH DE number 7000100