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
associated with the initial condition
. The main result (Theorem 2.4) gives a sufficient condition for the permanence, i.e., both
are bounded below and above by two positive constants.