The classification of the dynamical behavior of 3-dimensional type K monotone Lotka-Volterra systems
type: Item
instance of: scholarly article
title: The classification of the dynamical behavior of 3-dimensional type K monotone Lotka-Volterra systems
zbMATH Open document ID: 1022.34033
DOI: 10.1016/S0362-546X(01)00860-4
author: Xing Liang
author: Jifa Jiang
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-11-28T00:00:00Z
review text: The authors consider \(K\)-monotone Kolmogorov systems \(x_i'= x_i f_i(x)\) in \(\mathbb{R}^n\) ordered by a cone of the type \(K= \{(x_i): x_1,\dots, x_k\geq 0\), \(x_{k+1},\dots, x_n\leq 0\}\), where \(f\in C^1(\mathbb{R}^n_+, \mathbb{R}^n)\) is assumed to be such that solutions depend increasing on the initial value. The authors investigate attracting Lipschitz manifolds and hyperbolic equilibria of such systems. In particular, three-dimensional systems are studied, and the results are applied to classify three-dimensional \(K\)-monotone Lotka-Volterra systems.
reviewed by: Gerd Herzog
Mathematics Subject Classification ID: 34C12
zbMATH DE Number: 1836613
zbMATH Keywords: type \(K\) monotone
zbMATH Keywords: Kolmogorov systems
zbMATH Keywords: Lotka-Volterra systems
zbMATH Keywords: topological classification
MaRDI profile type: Publication
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full work available at URL: s0362-546x(01)00860-4
OpenAlex ID: W2063910457
description: scientific article; zbMATH DE number 1836613