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Dynamics of a three-species ratio-dependent diffusive model. (English) Zbl 1208.34070

Authors’ abstract: The authors investigate a nonautonomous ratio-dependent diffusive model of three species. By using the fixed point theorem of Brouwer and the theory of differential inequality and constructing a suitable Lyapunov function, sufficient conditions are obtained which guarantee the existence, uniqueness and stability of a positive periodic solution. The results of the analysis are complemented by numerical simulation.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34D05 Asymptotic properties of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
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