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

S. Blythe, R.M. Nisbet, William Gurney

Research output: Contribution to journalArticlepeer-review

59 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)147-176
Number of pages30
JournalTheoretical Population Biology
Issue number2
Publication statusPublished - Oct 1982


  • delay-differential equation
  • qualitative dynamics
  • population model


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