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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 Gurney et al in [Nature 287, 17–21 (1980)], together with a feedback control as considered by K. Gopalsamy and P. Weng [Int. J. Math. Sci. 16, No. 1, 177–192 (1993; Zbl 0765.34058)]. The authors consider the solution $\left(x\left(k\right),\mu \left(k\right)\right)$ associated with the initial condition $x\left(-m\right),x\left(-m+1\right),\cdots ,x\left(-1\right)\ge 0,x\left(0\right)$ and $\mu \left(0\right)>0$. The main result (Theorem 2.4) gives a sufficient condition for the permanence, i.e., both $x\left(k\right)$ and $\mu \left(k\right)$ are bounded below and above by two positive constants.
##### MSC:
 39A12 Discrete version of topics in analysis 92D25 Population dynamics (general) 93B52 Feedback control 39A11 Stability of difference equations (MSC2000)