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

202 Citations (Scopus)

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 2004

Fingerprint

Stage-structured
Predator-prey Model
Time Delay
Time delay
predators
Mortality
Resources
Stage Structure
Birth and Death Process
Population dynamics
Structured Populations
Population Dynamics
Linear Stability
population dynamics
Parturition
Model
death
Growth
Population

Keywords

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

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

A stage structured predator-prey model and its dependence on maturation delay and death rate. / Gourley, Stephen A.; Kuang, Yang.

In: Journal of Mathematical Biology, Vol. 49, No. 2, 08.2004, p. 188-200.

Research output: Contribution to journalArticle

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