Journal of Mathematical Biology

, Volume 49, Issue 2, pp 188–200 | Cite as

A stage structured predator-prey model and its dependence on maturation delay and death rate

  • Stephen A. Gourley
  • Yang Kuang


Many of the existing models on stage structured populations are single species models or models which assume a constant resource supply. In reality, growth is a combined result of birth and death processes, both of which are closely linked to the resource supply which is dynamic in nature. From this basic standpoint, we formulate a general and robust predator-prey model with stage structure with constant maturation time delay (through-stage time delay) and perform a systematic mathematical and computational study. Our work indicates that if the juvenile death rate (through-stage death rate) is nonzero, then for small and large values of maturation time delays, the population dynamics takes the simple form of a globally attractive steady state. Our linear stability work shows that if the resource is dynamic, as in nature, there is a window in maturation time delay parameter that generates sustainable oscillatory dynamics.

Key words or phrases:

Delay equation Stage structure Intraspecific competition Lyapunov functional Population model Through-stage death rate 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of SurreySurreyUK
  2. 2.Department of Mathematics and StatisticsArizona State UniversityTempeUSA

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