Massera's theorem for monotone dynamical systems in three dimensions
type: Item
instance of: scholarly article
title: Massera's theorem for monotone dynamical systems in three dimensions
zbMATH Open document ID: 1011.34023
DOI: 10.1016/S0022-247X(02)00039-2
author: Juan Campos
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-09-08T00:00:00Z
review text: The author studies the dynamical behaviour of increasing mappings \(f: \mathbb{R}^3\to \mathbb{R}^3\), where \(\mathbb{R}^3\) is ordered by a solid cone. It is proved that, if \(f\) is an increasing and orientation preserving homeomorphism, then either \(f\) has a fixed-point or each sequence with \(x_{n+1}= f(x_n)\) tends to infinity. This result is applied to ODEs \(x'= f(t,x)\), where \(f\) is \(T\)-periodic in \(t\) and quasimonotone increasing or decreasing in \(x\) with respect to the coordinate cone.
reviewed by: Gerd Herzog
Mathematics Subject Classification ID: 34C12
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 1797500
zbMATH Keywords: quasimonotone and monotone functions
zbMATH Keywords: initial value problems
zbMATH Keywords: periodic solutions
MaRDI profile type: Publication
cites work: The existence of periodic solutions of systems of differential equations
cites work: Periodic solutions to two-dimensional forced systems: The Massera theorem and its extension
cites work: An exclusion principle for periodic competitive systems in three dimensions
cites work: Massera's convergence theorem for periodic nonlinear differential equations
cites work: Abstract competitive systems and orbital stability in $\mathbf{{\mathbb R}^3}$
cites work: Q3742342
cites work: Q4834372
cites work: On the differential equations of species in competition
cites work: Homeomorphisms of the disk with trivial dynamics and extinction of competitive systems
cites work: Q5643279
cites work: Convergence to equilibrium on invariant \(d\)-hypersurfaces for strongly increasing discrete-time semigroups
cites work: Systems of differential equations which are competitive or cooperative: III. Competing species
cites work: Systems of Differential Equations That are Competitive or Cooperative. IV: Structural Stability in Three-Dimensional Systems
description: scientific article; zbMATH DE number 1797500