Stage-structured models of intra- and inter-specific competition within age classes

Jian Fang, Stephen A. Gourley, Yijun Lou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

16 Citations (Scopus)

Abstract

In some species, larvae and adults experience competition in completely different ways. Simple stage-structured models without larval competition usually yield a single delay equation for the adults. Using an age structured system incorporating competition among both larvae and adults, we derive a system of distributed delay equations for the numbers of larvae and adults. The system is neither cooperative nor reducible to a single equation for either variable. Positivity, boundedness and uniform strong persistence are established. Linear stability analysis of equilibria is difficult due to the strong coupling, but results are proved for small delays using monotone systems theory and exponential ordering. For small delay we prove a theorem on generic convergence to equilibria, which does not directly follow from standard theory but can be proved indirectly using comparison arguments. Finally, we consider an extension to two-strain competition and prove theorems on the linear stability of the boundary equilibria.
Original languageEnglish
Pages (from-to)1918-1953
Number of pages36
JournalJournal of Differential Equations
Volume260
Issue number2
DOIs
Publication statusPublished - 1 Jan 2016

Keywords

  • 34K12
  • 34K20
  • 34K25
  • 92D25
  • Competition
  • Delay
  • Exponential ordering
  • Monotone system
  • Stage structure

ASJC Scopus subject areas

  • Analysis

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