Estimating the boundary of the region of attraction of Lotka–Volterra system with time delays

This paper considers the local stability problem and estimates the region of attraction (RA) of the positive equilibrium of Lotka-Volterra (L-V) competitive system with time-delays. Based on the stability theory and the quadratic system theory, by choosing some less conservative integral inequalities and appropriate Lyapunov-Krasovskii (L-K) functional, a local stability condition is obtained by means of linear matrix inequalities (LMI) and the estimate of RA of the positive equilibrium is first discussed. Furthermore, the corresponding optimization problem for the estimate of RA is given. Numerical simulations show that the proposed stability condition in this paper is less conservative as compared with the most existing ones and the method of estimating RA is effective.