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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 (x(k),μ(k)) associated with the initial condition x(-m),x(-m+1),,x(-1)0,x(0) and μ(0)>0. The main result (Theorem 2.4) gives a sufficient condition for the permanence, i.e., both x(k) and μ(k) are bounded below and above by two positive constants.
MSC:
39A12Discrete version of topics in analysis
92D25Population dynamics (general)
93B52Feedback control
39A11Stability of difference equations (MSC2000)