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Permanence and stability in multi-species non-autonomous Lotka-Volterra competitive systems with delays and feedback controls. (English) Zbl 1165.34373

Summary: We consider a multi-species Lotka-Volterra type competitive system with delays and feedback controls. A general criterion on the permanence is established, which is described by integral form and independent of feedback controls. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solution to the model.

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
34K20 Stability theory of functional-differential equations
93B52 Feedback control
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