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Global Attractivity and Extinction of a Discrete Competitive System with Infinite Delays and Single Feedback Control

Author

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  • Yalong Xue
  • Xiangdong Xie
  • Qifa Lin
  • Fengde Chen

Abstract

A nonautonomous discrete two-species competition system with infinite delays and single feedback control is considered in this paper. Based on the discrete comparison theorem, a set of sufficient conditions which guarantee the permanence of the system is obtained. Then, by constructing some suitable discrete Lyapunov functionals, some sufficient conditions for the global attractivity and extinction of the system are obtained. It is shown that, by choosing some suitable feedback control variable, one of two species will be driven to extinction.

Suggested Citation

  • Yalong Xue & Xiangdong Xie & Qifa Lin & Fengde Chen, 2018. "Global Attractivity and Extinction of a Discrete Competitive System with Infinite Delays and Single Feedback Control," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-14, June.
    • Handle: RePEc:hin:jnddns:1893181
    DOI: 10.1155/2018/1893181
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