A stage structured predator-prey model and its dependence on maturation delay and death rate

Stephen A. Gourley, Yang Kuang

Research output: Contribution to journalArticle

206 Scopus citations

Abstract

Many of the existing models on stage structured populations are single species models or models which assume a constant resource supply. In reality, growth is a combined result of birth and death processes, both of which are closely linked to the resource supply which is dynamic in nature. From this basic standpoint, we formulate a general and robust predator-prey model with stage structure with constant maturation time delay (through-stage time delay) and perform a systematic mathematical and computational study. Our work indicates that if the juvenile death rate (through-stage death rate) is nonzero, then for small and large values of maturation time delays, the population dynamics takes the simple form of a globally attractive steady state. Our linear stability work shows that if the resource is dynamic, as in nature, there is a window in maturation time delay parameter that generates sustainable oscillatory dynamics.

Original languageEnglish (US)
Pages (from-to)188-200
Number of pages13
JournalJournal Of Mathematical Biology
Volume49
Issue number2
DOIs
StatePublished - Aug 1 2004

    Fingerprint

Keywords

  • Delay equation
  • Intraspecific competition
  • Lyapunov functional
  • Population model
  • Stage structure
  • Through-stage death rate

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics

Cite this