A stage structure model for the growth of a population involving switching and cooperation

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5 Citations (Scopus)

Abstract

We propose a theoretical model for a predator-prey interaction where the prey is a stage-structured population with varying maturity times for the immature stage. The interaction terms between immatures and adults are interpreted as cooperation. The predator consumes both the young and the adult of the prey and this prey population is more prone to predation at higher densities. The existence and stability of the equilibrium set are discussed. Using maturity time as a bifurcation parameter it is shown that Hopf bifurcation could occur.

Original languageEnglish
Pages (from-to)125-135
Number of pages11
JournalZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume82
Issue number2
DOIs
Publication statusPublished - 2002

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Stage Structure
Hopf bifurcation
Bifurcation (mathematics)
Prey
Model structures
Stage-structured
Structured Populations
Predator-prey
Predator
Interaction
Hopf Bifurcation
Theoretical Model
Time-varying
Bifurcation
Model
Term

Keywords

  • Cooperation
  • Hopf bifurcation
  • Predator
  • Prey
  • Switching
  • Time delay

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mechanics

Cite this

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AB - We propose a theoretical model for a predator-prey interaction where the prey is a stage-structured population with varying maturity times for the immature stage. The interaction terms between immatures and adults are interpreted as cooperation. The predator consumes both the young and the adult of the prey and this prey population is more prone to predation at higher densities. The existence and stability of the equilibrium set are discussed. Using maturity time as a bifurcation parameter it is shown that Hopf bifurcation could occur.

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