A result on a feedback system of ordinary differential equations
type: Item
instance of: scholarly article
title: A result on a feedback system of ordinary differential equations
zbMATH Open document ID: 0758.34035
DOI: 10.1007/BF01053804
author: A. S. Elkhader
published in: Journal of Dynamics and Differential Equations
publication date: 1993-01-16T00:00:00Z
review text: This paper deals with a feedback system of ordinary differential equations of the form \(x_ 1'=f_ 1(x_ 1,x_ n)\), \(x_ i'=f_ i(x_{i-1},x_ i,x_{i+1})\) \((2\leq i\leq n-1)\), \(x_ n'=f_ n(x_{n- 1},x_ n)\) where \(f_ i(i=1,2,\dots,n)\) satisfy some monotonicity conditions. The main result concerns the asymptotic behavior of bounded solutions. More specifically it is shown that the \(\omega\)-limit of such a solution contains at least one rest point or periodic point. An example for the case of an interacted 4-species model with linear per capita growth rate illustrates the result.
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34D45
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 94577
zbMATH Keywords: cyclic differential systems
zbMATH Keywords: omega-limit
zbMATH Keywords: feedback system of ordinary differential equations
zbMATH Keywords: asymptotic behavior
zbMATH Keywords: bounded solutions
zbMATH Keywords: periodic point
zbMATH Keywords: example
zbMATH Keywords: interacted 4-species model
reviewed by: George Karakostas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 94577