Dynamics of a neutral delay equation for an insect population with long larval and short adult phases

Stephen A. Gourley, Yang Kuang

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

We present a global study on the stability of the equilibria in a nonlinear autonomous neutral delay differential population model formulated by Bocharov and Hadeler. This model may be suitable for describing the intriguing dynamics of an insect population with long larval and short adult phases such as the periodical cicada. We circumvent the usual difficulties associated with the study of the stability of a nonlinear neutral delay differential model by transforming it to an appropriate non-neutral nonautonomous delay differential equation with unbounded delay. In the case that no juveniles give birth, we establish the positivity and boundedness of solutions by ad hoc methods and global stability of the extinction and positive equilibria by the method of iteration. We also show that if the time adjusted instantaneous birth rate at the time of maturation is greater than 1, then the population will grow without bound, regardless of the population death process.

Original languageEnglish (US)
Pages (from-to)4653-4669
Number of pages17
JournalJournal of Differential Equations
Volume246
Issue number12
DOIs
StatePublished - Jun 15 2009

Keywords

  • Global stability
  • Iteration method
  • Neutral delay equation
  • Population model

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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