Abstract.
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.
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Work is partially supported by NSF grant DMS-0077790.
Mathamatics Subject Classification (2000):92D25, 35R10
Revised version: 26 February 2004
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Gourley, S., Kuang, Y. A stage structured predator-prey model and its dependence on maturation delay and death rate. J. Math. Biol. 49, 188–200 (2004). https://doi.org/10.1007/s00285-004-0278-2
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DOI: https://doi.org/10.1007/s00285-004-0278-2