On the dynamics of two classes of periodic ecological models
type: Item
instance of: scholarly article
title: On the dynamics of two classes of periodic ecological models
zbMATH Open document ID: 0821.34042
DOI: 10.1016/0377-0427(94)90360-3
author: Philip Korman
published in: Journal of Computational and Applied Mathematics
publication date: 1995-09-25T00:00:00Z
review text: A Lotka-Volterra system of the type \(\dot x = x(a(t) - b(t)x - c(t)y)\), \(\dot y = y(d(t) - e(t)x - f(t)y)\) is considered. The coefficients of the system are \(p\)-periodic. The dynamics of this system is described in detail when the coefficients \(b,c,e,f\) are constant. For the cooperating- species case a complete description of the dynamics is obtained. For the predator-pray case the author derives a necessary and sufficient condition for existence of a positive \(p\)-periodic solution. For the equation \(\dot x = x(x - a(t)) (b(t) - x)\) sufficient conditions for existence of two positive \(p\)-periodic solutions are found. Moreover \(0 \leq x_ 1 (t) \leq x_ 2 (t)\) for all \(t\) and \(\min_ t a(t) \leq x_ 1 (t) \leq \max_ t a(t)\), \(\min_ t b(t) \leq x_ 2 (t) \leq \max_ t b(t)\).
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 92D40
zbMATH DE Number: 711770
zbMATH Keywords: periodic solutions
zbMATH Keywords: Lotka-Volterra system
zbMATH Keywords: predator-pray case
reviewed by: Angel B. Dishliev
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90360-3
OpenAlex ID: W1972809903
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description: scientific article; zbMATH DE number 711770