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Almost sufficient and necessary conditions for permanence and extinction of nonautonomous discrete logistic systems with time-varying delays and feedback control

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Abstract

A class of nonautonomous discrete logistic single-species systems with time-varying pure-delays and feedback control is studied. By introducing a new research method, almost sufficient and necessary conditions for the permanence and extinction of species are obtained. Particularly, when the system degenerates into a periodic system, sufficient and necessary conditions on the permanence and extinction of species are obtained. Moreover, a very important fact is found in our results, that is, the feedback control and delays are harmless for the permanence and extinction of species for discrete single-species systems. This shows that in a discrete single-species system introducing the feedback control to factitiously control the permanence and extinction of species is useless.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, P.R. China

    Jiabo Xu & Zhidong Teng

  2. College of Mathematics and Computer Science, Gannan Normal University, Ganzhou, 341000, P.R. China

    Shujing Gao

Authors
  1. Jiabo Xu
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  2. Zhidong Teng
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  3. Shujing Gao
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Correspondence to Jiabo Xu.

Additional information

Supported by The National Natural Science Foundation of P.R. China (10961022, 10901130), The Scientific Research Programmes of Colleges in Xinjiang (XJEDU2007G01, XJEDU2006I05, XJEDU2008S10).

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Xu, J., Teng, Z. & Gao, S. Almost sufficient and necessary conditions for permanence and extinction of nonautonomous discrete logistic systems with time-varying delays and feedback control. Appl Math 56, 207–225 (2011). https://doi.org/10.1007/s10492-011-0003-6

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  • DOI: https://doi.org/10.1007/s10492-011-0003-6

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