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Permanence and stability of equilibrium for a two-prey one-predator discrete model. (English) Zbl 1123.39012
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.

39A12 Discrete version of topics in analysis
39A11 Stability of difference equations (MSC2000)
92D25 Population dynamics (general)
Full Text: DOI
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