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J Math Biol. 2004 Aug;49(2):188-200. Epub 2004 May 31.

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

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  • 1Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey GU2 7XH, UK. s.gourley@surrey.ac.uk

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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