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Instability and complex dynamic behaviour in population models with long time-delays

Blythe, S. and Nisbet, R.M. and Gurney, William (1982) Instability and complex dynamic behaviour in population models with long time-delays. Theoretical Population Biology, 22 (2). pp. 147-176. ISSN 0040-5809

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Abstract

Some of the properties of the delay-differential equation , where R and D represent the rates of recruitment to, and death from, an adult population of size X, with maturation period τ are examined. The biological constraints upon these recruitment and death functions are specified, and they are used to establish results on stability, boundedness, and persistent fluctuations of limit cycle type. The relationship between models based on delay-differential and difference equations is then explored, and it is shown how well-established results on period-doubling and chaotic behaviour in the latter can yield insight into the qualitative dynamics of the former. Using numerical studies of two population models with differing forms of recruitment function, we show how, by making use of our results, it is possible to simplify the analysis of delay-differential equation population models.

Item type: Article
ID code: 41612
Keywords: delay-differential equation, qualitative dynamics, population model, Probabilities. Mathematical statistics, Ecology, Evolution, Behavior and Systematics
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Pure Administrator
    Date Deposited: 19 Oct 2012 18:59
    Last modified: 05 Sep 2014 18:22
    URI: http://strathprints.strath.ac.uk/id/eprint/41612

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