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Zbl 1055.92043
Gourley, Stephen A.; Kuang, Yang
A stage structured predator-prey model and its dependence on maturation delay and death rate. (English)
[J] J. Math. Biol. 49, No. 2, 188-200 (2004). ISSN 0303-6812; ISSN 1432-1416/e

Summary: 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.

MSC 2000:: *92D25 Population dynamics
34K60 Applications of functional-differential equations
34K20 Stability theory of functional-differential equations
92D40 Ecology

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Zentralblatt MATH Berlin [Germany]