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Exponential stability of a competitive Lotka-Volterra system with delays. (English) Zbl 1143.92040
Summary: The exponential stability of a two-species competitive Lotka-Volterra system with discrete delays has been studied. By constructing an appropriate Lyapunov functional and using the linear matrix inequality (LMI) optimization approach, a series of sufficient criteria is obtained which ensure the exponential stability of the positive equilibrium of the given Lotka-Volterra system. The results are new and improve some earlier work. An illustrative example is given to demonstrate the effectiveness of the obtained results.

MSC:
92D40 Ecology
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations
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