Geodesic
Almost sufficient and necessary conditions for permanence and extinction of nonautonomous discrete logistic systems with time-varying delays and feedback control
Applications of Mathematics, Tome 56 (2011) no. 2, pp. 207-225.

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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.
DOI : 10.1007/s10492-011-0003-6
Classification : 39A22, 39A30, 92D25, 93B52
Keywords: discrete system; permanence; extinction; feedback control; time-varying delay 
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     title = {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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Xu, Jiabo; Teng, Zhidong; Gao, Shujing. Almost sufficient and necessary conditions for permanence and extinction of nonautonomous discrete logistic systems with time-varying delays and feedback control. Applications of Mathematics, Tome 56 (2011) no. 2, pp. 207-225. doi : 10.1007/s10492-011-0003-6. http://geodesic.mathdoc.fr/articles/10.1007/s10492-011-0003-6/

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