Convergence in lotka-volterra-type delay systems without instantaneous feedbacks

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

Most of the convergence results appearing so far for delayed Lotka-Volterra-type systems require that undelayed negative feedback dominate both delayed feedback and interspecific interactions. Such a requirement is rarely met in real systems. In this paper we present convergence criteria for systems without instantaneous feedback. Roughly, our results suggest that in a Lotka-Volterra-type system if some of the delays are small, and initial functions are small and smooth, then the convergence of its positive steady state follows that of the undelayed system or the corresponding system whose instantaneous negative feedback dominates. In particular, we establish explicit expressions for allowable delay lengths for such convergence to sustain.

Original languageEnglish (US)
Pages (from-to)45-58
Number of pages14
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume123
Issue number1
DOIs
StatePublished - Jan 1 1993

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Convergence in lotka-volterra-type delay systems without instantaneous feedbacks'. Together they form a unique fingerprint.

  • Cite this