This paper considers the existence of periodic solutions for shunting inhibitory cellular neural networks (SICNNs) with neutral delays. By applying the theory of abstract continuation theorem of

It is well known that SICNNs have been extensively applied in psychophysics, speech, perception, robotics, adaptive pattern recognition, vision, and image processing. The dynamical behaviors of SICNNs with delays have been widely investigated in recent years. A large number of important results on the dynamical behaviors of SICNNs have been established and successfully applied to signal processing, pattern recognition, associative memories, and so on. In particular, there exist many results on the existence and stability of periodic and almost periodic solutions for SICNNs with delays. We refer the reader to [

On the other hand, the stability analysis of various neutral delay-differential systems has drawn much research attention [

Motivated by the above, we consider shunting inhibitory cellular neural networks with neutral delays described by

By using the Lyapunov functions and linear matrix inequality approach (LMI), most authors studied the asymptotic stability or exponential stability of the equilibrium point (see [

The initial conditions of (

For the sake of convenience, we denote

The main purpose of this paper is to obtain some sufficient conditions for the existence of the periodic solutions for system (

Throughout this paper, for

function

there exists positive constant

In order to study (

Let

Let

Then there is a

In order to use Lemma

Let

It is easy to see that

The differential operator

If

The proof of Lemma

Let

Suppose that

Throughout this paper, we assume that

Set

Suppose that

We consider the operator equation _{5}), we have

Integrating both sides of (

Similarly,

Thus, for all

Denote

Considering assumption (H_{4}), we know

Therefore, by using Lemma

In this section, we give two examples to demonstrate the results obtained in previous sections.

Consider the following shunting inhibitory cellular neural networks with neutral delays:

Let _{1})–(H_{3}) hold and

Let

It is easy to see that (H_{4}) and (H_{5}) hold. Therefore, all conditions of Theorem

Let _{1})–(H_{3}) hold and

Let

It is easy to see that (H_{4}) and (H_{5}) hold. Therefore, all conditions of Theorem

In this paper, a class of neutral type shunting inhibitory cellular neural networks is investigated by means of an abstract continuous theorem of

The author is grateful to the referees for their suggestions on the first draft of the paper. This work was supported by the scientific research fund of Fujian Provincial Education Department (JA11309).