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The qualitative analysis of \(n\)-species nonlinear competition systems with feedback control and periodic coefficients. (Chinese. English summary) Zbl 1078.92068

Summary: A nonautonomous multispecies periodic coefficient, nonlinear relation, competitive system with feedback control is studied. By making use of the comparison theorem and the Brouwer fixed point theorem, we obtain the boundedness of positive solutions of the system and the existence of positive periodic solutions. After that, by constructing a suitable Lyapunov function, sufficient conditions which guarantee the global asymptotic stability of the periodic solutions are obtained.

MSC:

92D40 Ecology
93D15 Stabilization of systems by feedback
34D05 Asymptotic properties of solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
37N25 Dynamical systems in biology
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