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

Yang Kuang, Hal Smith

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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
Issue number1
StatePublished - 1993

ASJC Scopus subject areas

  • Mathematics(all)


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