Stability analysis of the time delay in a host-parasitoid model

Virginia Dale Adams, Donald L. DeAngelis, Robert A. Goldstein

Research output: Contribution to journalArticle

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Abstract

The effect of a time delay on the local stability of a host-parasitoid model is analyzed. The delay is between the time of parasitization of the host and the emergence of the parasitoid from the host. Both analytic methods and computer simulations are used in this study. By linearizing and transforming the original equations, sufficient conditions for the local stability are found. In the case of the parameters considered, the results illustrate the destabilizing effect of the time delay. As the lag increases the number of stable points decreases and the points become more scattered in the parameter space. Simulations of the original model are also produced. The region of stability indicated by the simulations is greater than that predicted by the use of the analytic technique. The analysis also reveals the impact of the population parameters upon the stability of the time delay model. The importance of understanding time lags is discussed with reference to population regulation.

Original languageEnglish (US)
Pages (from-to)43-62
Number of pages20
JournalJournal of theoretical biology
Volume83
Issue number1
DOIs
StatePublished - Mar 7 1980

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ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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