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Permanence for a discrete Nicholson’s blowflies model with feedback control and delay. (English) Zbl 1163.39011
The authors discuss the discrete Nicholson’s blowflies model with feedback control, which is a discrete form of its continuous model considered by {\it W. S. C. Gurney} et al. in [Nature 287, 17--21 (1980), \url{doi:10.1038/287017a0}], together with a feedback control as considered by {\it K. Gopalsamy} and {\it P. Weng} [Int. J. Math. Sci. 16, No. 1, 177--192 (1993; Zbl 0765.34058)]. The authors consider the solution $(x(k), \mu(k))$ associated with the initial condition $x(-m), x(-m+1),\dots, x(-1)\ge 0$, $x(0)$ and $\mu(0)>0$. The main result (Theorem 2.4) gives a sufficient condition for the permanence, i.e., both $x(k)$ and $\mu(k)$ are bounded below and above by two positive constants.

39A12Discrete version of topics in analysis
92D25Population dynamics (general)
93B52Feedback control
39A22Growth, boundedness, comparison of solutions (difference equations)
39A30Stability theory (difference equations)
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