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This paper investigates the synchronization problem of neural networks with mixed time delays under information constrains. The designed synchronization scheme is built on the framework of hybrid systems. Besides including nonuniform sampling, some other characteristics, such as quantization, transmission-induced delays, and data packet dropouts, are also considered. The sufficient condition that depended on network characteristics is obtained to guarantee the remote asymptotical synchronization of neural networks with mixed time delays. A numerical example is given to illustrate the validity of the proposed method.

Recently, neural networks have been widely studied by many scholars due to its potential applications in pattern recognition, image processing, signal processing, biology engineering, and information science [

Generally, some useful approaches can be utilized for the synchronization problem of neural networks, which include passivity analysis [

Consider the following general master-slave neural network with mixed time delays [

For

The neuron activation functions are bounded.

Let the error be

The above controller (

A quantizer is called logarithmic if the set of quantized levels is characterized by

The quantizer is assumed to be symmetric; that is,

Generally,

There exist three constants

Set

In this section, the stability of the error system (

Let

For any constant symmetric matrix

Given scalars

Construct the following Lyapunov functional as

Because the uncertain matrix

Given scalars

Utilizing Schur formula and matrix inequality

In the above process, the free-weighting matrix technology is applied to complete the proof. Moreover, similar to [

In this section, a numerical example is given to demonstrate the effectiveness of the proposed synchronization scheme.

Consider the following master-slave neural network with mixed time delays as in [

The chaotic behaviors of the master and slave systems are given in Figures

Chaotic behavior of the master system.

Chaotic behavior of the slave system with

Similar to [

State response curves of the error system.

In the present works, the networked synchronization scheme for master-slave neural networks with mixed time delays has been proposed. The error system can be stabilized under information constraints. The obtained result depends on network characteristics. In future works, more performance requirements for synchronization of master-slave neural networks with mixed time delays will be considered in a uniform network topological structure.

This work is supported by the Natural Science Foundation of China under Grant 61203076, the Natural Science Foundation of Tianjin City under Grant 13JCQNJC03500, the Natural Science Foundation of Hebei Province under Grant F2012202100, and the Excellent Young Technological Innovation Foundation Project in Hebei University of Technology under Grant 2011005.