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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.

##### MSC:
 39A12 Discrete version of topics in analysis 39A11 Stability of difference equations (MSC2000) 92D25 Population dynamics (general)
##### Keywords:
predator-prey system; equilibrium; stability; permanence
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##### References:
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