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A class of fuzzy neural networks (FNNs) with time-varying delays and impulses is investigated. With removing some restrictions on the amplification functions, a new differential inequality is established, which improves previouse criteria. Applying this differential inequality, a series of new and useful criteria are obtained to ensure the existence of global robust attracting and invariant sets for FNNs with time-varying delays and impulses. Our main results allow much broader application for fuzzy and impulsive neural networks with or without delays. An example is given to illustrate the effectiveness of our results.

The theoretical and applied studies of the current neural networks (CNNs) have been a new focus of studies worldwide because CNNs are widely applied in signal processing, image processing, pattern recognition, psychophysics, speech, perception, robotics, and so on. The scholars have introduced many classes of CNNs models such as Hopfield-type networks [

It is well known that local field neural network not only models Hopfield-type networks but also models bidirectional associative memory networks and cellular neural networks. In the past few years, there has been increasing interest in studying dynamical characteristics such as stability, persistence, periodicity, robust stability of equilibrium points, and domains of attraction of local field neural network. Many deep theoretical results have been obtained for local field neural network. We can refer to [

However, in mathematical modeling of real world problems, we will encounter some other inconveniences, for example, the complexity and the uncertainty or vagueness. Fuzzy theory is considered as a more suitable setting for the sake of taking vagueness into consideration. Based on traditional cellular neural networks (CNNs),T. Yang and L.-B. Yangproposed the fuzzy CNNs (FCNNs) [

The main purpose of this paper is to investigate the global robust attracting and invariant sets of FNNs (

The rest of this paper is organized as follows. In Section

As usual,

Let

As usual, in the theory of impulsive differential equations, at the points of discontinuity

Inspired by [

Throughout this paper, we always assume the following.

For all

The activation function

Functions

Let

Assume

If

If

Firstly, let us prove (i). For a given

Next, we prove (ii). Since

Let

For any given

For any given

For a class of differential equations with the term of fuzzy AND and fuzzy OR operation, there is the following useful inequality.

Let

In this section, we will establish a new nonlinear delay differential inequality which will play the important role to prove our main results.

Assume that

For any constant

provided that

Consider that

provided that

where

Since

If (

Since

By

By the process of proof of Lemma

Under the conditions of Lemma

In this section, we will state and prove our main results. The following lemma is very useful to prove Theorem

Assume that

In fact, by the assumption

Assume that (

Calculating the upper right derivative

According to Lemma

On the other hand, since

Then by (

In addition to (

The following illustrative example will demonstrate the effectiveness of our results. Consider the following FNNs with time-varying delays and impulses:

The author would like to thank the anonymous referees for their useful and valuable suggestions. This work is supported by the National Natural Sciences Foundation of China under Grant no. 11161025, Yunnan Province Natural Scientific Research Fund Project (no. 2011FZ058), and Yunnan Province Education Department Scientific Research Fund Project (no. 2011Z001).