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Existence, uniqueness and stability of positive periodic solution for a nonlinear prey-competition model with delays. (English) Zbl 1104.34050
The authors study an \(n\times n\) nonquadratic periodic prey-competition ODE model with delays in which the \(m\) preys are competitors and the \(n-m\) predators are competitors, respectively. The variable coefficients in the model are assumed to be continuous periodic functions on \([0,+\infty)\) with a common period. This model is more general and more complicated than the traditional Lotka-Volterra system and some recent nonquadratic prey-competition models. The authors provide sufficient conditions for the existence of a unique globally attractive positive periodic solution and a few examples of applications of the model in population dynamics.

MSC:
34K13 Periodic solutions to functional-differential equations
92D25 Population dynamics (general)
34K20 Stability theory of functional-differential equations
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