Dynamics of hierarchical models in discrete-time

S. R.J. Jang, J. M. Cushing

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

We derive and analyze a general class of difference equation models for the dynamics of hierarchically organized populations. Different forms of intra-specific competition give rise to different types of nonlinearities. For our models, we prove that contest competition results asymptotically in only equilibrium dynamics. Scramble competition, on the other hand, can result in more complex asymptotic dynamics. We study both the case when the limiting resource is a constant and when it is dynamically modeled. We prove, in all cases, that the population persists if the inherent net reproductive number of the population is greater than one.

Original languageEnglish (US)
Pages (from-to)95-115
Number of pages21
JournalJournal of Difference Equations and Applications
Volume11
Issue number2
DOIs
StatePublished - Feb 1 2005

Keywords

  • Discrete-time model
  • Inherent net reproductive number
  • Intra-specific competition
  • Uniform persistence

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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