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Sufficient conditions are established for the permanence in a delayed Nicholson’s blowflies model with feedback control on time scales. Our investigation confirms that the bounded feedback terms do not have any influence on the permanence of this system.

In 2008, we considered the following discrete Nicholson’s blowflies model with feedback control (see [

Assume that

The continuous and discrete systems always appear separately, until in 1988, the theory of time scales, which has recently received much attention, was initiated by Hilger [

For the origin of mathematical model for Nicholson’s blowflies, one can see [

In this paper, we will discuss the permanence of the following system:

We assume that

When

When

In what follows we shall use the notations

Before giving our main result, first we list some basic properties about time scales which could be found in ([

A time scale is an arbitrary nonempty closed subset

For

Define the interval

A function

Assume

If

We say that a function

If

For

When

If

Suppose

Assume that

Suppose

In order to give our main result, we also need to establish the following definitions and lemmas. The first definition is the generalized version of the semicycle in discrete situation [

Let

The following two lemmas could be found in [

Assume that

(1)

(2)

Assume that

(1)

(2)

Before giving our main result, we list the definition of uniform ultimate boundedness.

Solutions for system (

First, we give a lemma which will be useful for our further discussion.

Let

The exponential form

In the sequel, we assume that

Assume that (

We now prove the following result before proving Theorem

Assume that (

We divided the proof into four claims.

(1) There exists some

(2) There exists some

(3) For simplicity, set

By Claims 1 and 2 and the first equation of system (

Set

Choose

If the coefficient functions

If all the conditions in Theorem

No data were used to support this study.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

All authors contributed equally to this work. All authors read and approved the final manuscript.

This work is supported by NSF of China (11201213, 11371183), NSF of Shandong Province (ZR2015AM026), and the Project of Shandong Provincial Higher Educational Science and Technology (J15LI07).