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 W. S. C. Gurney et al. in [Nature 287, 17–21 (1980), doi:10.1038/287017a0], 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 \((x(k), \mu(k))\) associated with the initial condition \(x(-m), x(-m+1),\dots, x(-1)\geq 0\), \(x(0)\) 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.


39A12 Discrete version of topics in analysis
92D25 Population dynamics (general)
93B52 Feedback control
39A22 Growth, boundedness, comparison of solutions to difference equations
39A30 Stability theory for difference equations


Zbl 0765.34058
Full Text: DOI


[1] DOI: 10.1038/287017a0
[2] Gopalsamy K., Int. J. Math. Sci. 1 pp 177–
[3] Lalli B. S., Dynam. Syst. Appl. 5 pp 117–
[4] DOI: 10.1006/jmaa.2000.7420 · Zbl 1003.34069
[5] DOI: 10.1016/j.cam.2004.11.002 · Zbl 1069.34100
[6] Wang L. L., J. Lanzhou Univ. (Nat. Sci.) 42 pp 114–
[7] DOI: 10.1016/j.jmaa.2005.04.036 · Zbl 1107.39017
[8] Chen F. D., Appl. Math. Comput. 186 pp 23–
[9] DOI: 10.1016/j.aml.2006.08.023 · Zbl 1128.92029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.