Permanence of a nonlinear prey-competition model with delays.

*(English)*Zbl 1131.92062Summary: A nonlinear periodic predator-prey model with \(m\)-preys and \((n - m)\)-predators and delays is studied, which can be seen as the modification of the traditional Lotka-Volterra prey-competition model. Two sets of sufficient conditions which guarantee the permanence of the system are obtained. One set is delay independent, while the other set is delay dependent. Our results supplement those obtained by F. D. Chen, X. Xie and J. Shi [Existence, uniqueness and stability of positive periodic solution for a nonlinear prey-competition model with delays. J. Comput. Appl. Math. 194, No. 2, 368–387 (2006; Zbl 1104.34050)].

##### MSC:

92D40 | Ecology |

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

34K20 | Stability theory of functional-differential equations |

##### Keywords:

nonautonomous
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\textit{A. Huang}, Appl. Math. Comput. 197, No. 1, 372--381 (2008; Zbl 1131.92062)

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##### References:

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