Qualitative permanence of Lotka–Volterra equations

摘要

In this paper, we consider permanence of Lotka–Volterra equations. We investigate the sign structure of the interaction matrix that guarantees the permanence of a Lotka–Volterra equation whenever it has a positive equilibrium point. An interaction matrix with this property is said to be qualitatively permanent. Our results provide both necessary and sufficient conditions for qualitative permanence.