Stable equilibrium of systems of generalized Volterra type

AbstractIn this paper, the global stability of systems of the generalized Volterra type: dxidt=xi∑j=1naijxj+bi, i=1,…,n. is investigated. It is shown that a stable equilibrium point of (1) must be a solution of corresponding linear complementarity problem. Further, when the structure of (1) is restricted, the known stability condition is proved to be necessary and sufficient for the existence of a stable equilibrium point for every b ϵ Rn. Some structures satisfying these restrictions are given