Asymptotic behavior of quasi-competitive species defined by Lotka-Volterra dynamics
type: Item
instance of: scholarly article
title: Asymptotic behavior of quasi-competitive species defined by Lotka-Volterra dynamics
zbMATH Open document ID: 0853.34034
DOI: 10.1007/BF02007173
author: Gang Lü
author: B. D. Sleeman
published in: Acta Mathematicae Applicatae Sinica. English Series
publication date: 1997-01-13T00:00:00Z
review text: The paper studies the dynamical behaviour of three-dimensional Lotka-Volterra systems \[ dx_i (t)/dt = x_i \left( r_i + \sum^3_{j = 1} a_{ij} x_j \right)\;(i = 1,2,3) \] satisfying \(r_1 = r_2 = r_3 > 0\); \(a_{11}, a_{22}, a_{33} < 0\), \(a_{ij}/a_{jj} + a_{ji}/a_{ii} = \beta > 0\) \((i \neq j\); \(i,j = 1,2,3)\). Dynamical behaviour includes, depending on the parameter values, globally stable coexistence equilibrium, periodic oscillations of the three species, extinction of two species, and extinction of the three species through nonperiodic oscillations (May-type trajectories).
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 883519
zbMATH Keywords: three-dimensional Lotka-Volterra systems
zbMATH Keywords: coexistence
zbMATH Keywords: periodic oscillations
zbMATH Keywords: extinction
reviewed by: Carlos A. dos Santos Braumann
MaRDI profile type: Publication
cites work: Asymptotic Behaviors in the Dynamics of Competing Species
cites work: Nonlinear Aspects of Competition Between Three Species
cites work: Global stability and oscillations in classical Lotka-Volterra loops
cites work: On $\omega $-Limits for Competition Between Three Species
cites work: On the differential equations of species in competition
description: scientific article; zbMATH DE number 883519