Computer aided proof for the global stability of Lotka-Volterra systems

By modifying the mechanical method of determining LaSalleʹs invariant sets for Lotka-Volterra chain systems [1,2] and repeatedly using Wuʹs characteristic set method [3,4], it is proved that for a class of Lotka-Volterra loop systems, the locally asymptotically stable positive equilibrium point must be globally stable.