Global Stability for N-species Lotka-Volterra Systems with Delay, II: Reducible Cases, Sufficiency and Necessity 1)

Abstract. in this paper, an n-species delayed Lotka-Volterra system without delayed intraspecific competitions is considered. It is proved that the system is globally stable for all off-diagonal delays τij ≥ 0 if and only if the interaction matrix A of the system satisfies Condition (WDD). 1