Abstract
In this paper, we revisit the famous Lotka-Volterra competitive system. By combining spectral matrix theory with Lyapunov function, some new sufficient conditions are obtained to guarantee the global asymptotic stability of a unique equilibrium for Lotka-Volterra competitive system. Our new results generalize and significantly improve the known results in the previous literature. The main purpose of this paper is to propose a new methodology to study the high-dimensional Lotka-Volterra system. And this method can be extensively used to study the global asymptotic stability of the equilibrium. Finally, some examples and their simulations show the feasibility and effectiveness of our results.
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