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Global attractivity in an almost periodic multi-species nonlinear ecological model. (English) Zbl 1099.92069
Summary: A nonlinear almost periodic predator-prey model with \(n\)-preys and \(m\)-predators is studied, which can be seen as the modification of the traditional multi-species Lotka-Volterra predator-prey model. For the general nonautonomous case, by using differential inequality theory, we obtain the sufficient conditions which guarantee the uniform persistence and nonpersistence of the system. After that, by constructing a suitable Lyapunov function, some sufficient conditions are obtained which ensure the global attractivity of the system. For the almost periodic case, by constructing a suitable Lyapunov function, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained. Examples together with their numeric simulations show the feasibility of our main results.

MSC:
92D40 Ecology
34A40 Differential inequalities involving functions of a single real variable
34C27 Almost and pseudo-almost periodic solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
34D20 Stability of solutions to ordinary differential equations
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