Intra-specific competition and insect larval development: A model with time-dependent delay

Stephen A. Gourley, Rongsong Liu, Yijun Lou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


We derive a stage-structured model for an insect population in which a larva matures on reaching a certain size, and in which there is intra-specific competition among larvae that hinders their development, thereby prolonging the larval phase. The model, a system of delay differential equations for the total numbers of adults and larvae, assumes two forms. One of these is a system with a variable state-dependent time delay determined by a threshold condition, the other has constant and distributed delays, a size-like independent variable replacing time t, and no threshold condition. We prove theorems on boundedness and on the linear stability of equilibria.
Original languageEnglish
Pages (from-to)353-369
Number of pages17
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Issue number2
Publication statusPublished - 1 Apr 2017


  • Boundedness
  • competition
  • Delay
  • Size-structure
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)

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