Exponential stability of a competitive Lotka–Volterra system with delays

摘要

In this paper, the exponential stability of a two-species competitive Lotka–Volterra system with discrete delays has been studied. By constructing 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.