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Existence of almost periodic solution in a ratio-dependent Leslie system with feedback controls. (English) Zbl 1145.34026
The authors consider a predator-prey model represented by a ratio-dependent Leslie system with linear feedback controls and with almost periodic coefficients. Deriving auxiliary results on the logistic equation and using a comparison theorem, they first prove that the system under discussion has at least one positive bounded solution. A further result, obtained by an appropriate Lyapunov function, yields the existence of a unique positive almost periodic and globally attractive solution. This latter solution is even periodic if all the coefficients of the system are assumed to be periodic. The main result is illustrated by a numerical example.
MSC:
34C60Qualitative investigation and simulation of models (ODE)
92D25Population dynamics (general)
34C27Almost and pseudo-almost periodic solutions of ODE
34C25Periodic solutions of ODE
34C11Qualitative theory of solutions of ODE: growth, boundedness
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