The number and stability of limit cycles for planar piecewise linear systems of node-saddle type
type: Item
instance of: scholarly article
title: The number and stability of limit cycles for planar piecewise linear systems of node-saddle type
zbMATH Open document ID: 1429.34037
author: Jiafu Wang
author: Xiaoyan Chen
author: Lihong Huang
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-10-18T00:00:00Z
review text: The autors study limit cycles of the piecewise linear system \[ \dot{\mathbf{x}} =\begin{cases} \begin{pmatrix} T^+ & -1 \\ D^+& 0 \end{pmatrix} \mathbf{x} + \begin{pmatrix} -b\\ a^+ \end{pmatrix}, \quad x >0\\ \begin{pmatrix} T^- & -1 \\ D^- & 0 \end{pmatrix} \mathbf{x} + \begin{pmatrix} 0\\ a^-\end{pmatrix}, \quad x <0, \end{cases} \] where \((x,y)^t \in \mathbb{R}^2\). They find the parameter regions, where the system has one limit cycle, two limit cycles or does not have limit cycles. The stability of the limit cycles is investigated as well.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 6957997
zbMATH Keywords: limit cycle
zbMATH Keywords: Poincaré-Bendixon theorem
zbMATH Keywords: stability
zbMATH Keywords: piecewise linear differential systems
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.09.024
OpenAlex ID: W2889668533
cites work: Piecewise-smooth dynamical systems. Theory and applications
cites work: Saddle-node bifurcation of invariant cones in 3D piecewise linear systems
cites work: Neuronal Networks with Gap Junctions: A Study of Piecewise Linear Planar Neuron Models
cites work: On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line
cites work: Q3994508
cites work: Canonical Discontinuous Planar Piecewise Linear Systems
cites work: A general mechanism to generate three limit cycles in planar Filippov systems with two zones
cites work: On Hopf bifurcation in non-smooth planar systems
cites work: On the number of limit cycles in general planar piecewise linear systems
cites work: Existence of limit cycles in general planar piecewise linear systems of saddle-saddle dynamics
cites work: On the number of limit cycles in general planar piecewise linear systems of node-node types
cites work: On the basins of attraction for a class of delay differential equations with non-monotone bistable nonlinearities
cites work: Centennial History of Hilbert's 16th Problem
cites work: Q5251027
cites work: On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry
cites work: On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities
cites work: Lower bounds for the maximum number of limit cycles of discontinuous piecewise linear differential systems with a straight line of separation
cites work: Uniqueness of limit cycles for sewing planar piecewise linear systems
cites work: The qualitative analysis of a class of planar Filippov systems
DOI: 10.1016/J.JMAA.2018.09.024
description: scientific article; zbMATH DE number 6957997