Permanence and stability of equilibrium for a two-prey one-predator discrete model (Q878918)

The authors study a discrete two-prey one-predator model. First, sufficient conditions for the permanence of the system are established. Then a sufficient and necessary condition for the local asymptotic stability of an equilibrium is provided. However, it should be pointed out that assumption (H3) should be \(\frac {\underline{C}m_1+\underline{D}m_2}{1+\overline{A}M_1+\overline {B}M_2}>\overline{d}\). Also, by Proposition 2.6, it seems to the reviewer that the conclusion in Theorem 2.7 should be persistence rather than permanence.