Global structure for a class of dynamical systems
type: Item
instance of: scholarly article
title: Global structure for a class of dynamical systems
zbMATH Open document ID: 0985.37018
DOI: 10.1016/S0960-0779(98)00184-2
author: Suochun Zhang
author: Zuohuan Zheng
published in: Chaos, Solitons and Fractals
publication date: 2000-08-09T00:00:00Z
review text: The authors consider the ordinary differential equations in the plane \[ {dx\over dt}= X(x,y),\quad {dy\over dt}= Y(x,y),\tag{1} \] where \(X(x,y)\), \(Y(x,y)\) are continuous, and (1) satisfies the existence and uniqueness of solutions for the initial value problem. They are mainly interested in the global structure of positive bounded systems on the plane which have \(m\) singular points, but no closed orbits and singular closed orbits. The authors prove that these systems have at least \(m-1\) connecting orbits and all the connecting orbits, homoclinic orbits and singular points form a compact simply connected set. They study the asymptotic behaviour of these orbits as \(t\to\pm\infty\).
Mathematics Subject Classification ID: 37C29
Mathematics Subject Classification ID: 34C37
zbMATH DE Number: 1486536
zbMATH Keywords: singular point
zbMATH Keywords: closed orbit
zbMATH Keywords: connecting orbit
zbMATH Keywords: singular closed orbit
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: The existence of trajectories joining critical points
cites work: Q4712760
cites work: Viscosity matrices for two‐dimensional nonlinear hyperbolic systems
cites work: Isolated Invariant Sets and Isolating Blocks
cites work: Q4180600
cites work: Q4392094
cites work: Global Structure of Ordinary Differential Equations in the Plane
cites work: Global structure of continuous flows on 2-manifolds
cites work: On the existence and uniqueness of connecting orbits for cooperative systems
cites work: Trajectories joining critical points
cites work: Q4848049
cites work: On the limit cycles for a class of planar systems
cites work: On the existence of closed orbits for a differential system
cites work: Q4514303
full work available at URL: s0960-0779(98)00184-2
OpenAlex ID: W1989851007
description: scientific article; zbMATH DE number 1486536