Computer aided proof for the global stability of Lotka-Volterra systems (Q1921255)

The Lotka-Volterra system \[ \dot x_i= x_i \sum^n_{j=1} a_{ij} (x_j-x_j^*), \quad i=1,2, \dots, n, \] is considered. The problem of stability of the equilibrium state \(x^*\) is solved in terms of the modification of LaSalle's invariance principle and Wu's characteristic set method [\textit{W.-T. Wu}, Sci. Sinica 21, 159-172 (1978; Zbl 0376.68057)].