Necessary-sufficient conditions for permanence and extinction in lotka-volterra system with distributed delays

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Abstract

In this paper, the necessary and sufficient conditions for permanence and extinction of the autonomous two-species Lotka-Volterra system with distributed delays are given. Some previous results are improved and extended. Moreover, it is shown in our paper that the permanence and extinction of the distributed-delayed system is equivalent to that of its nondelayed system.

Keywords

Necessary and sufficient conditions
Lotka-Volterra system
Distributed delays
Extinction
Permanence

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This work is supported by National Natural Science Foundation of China.