Adaptive synchronization of a class of chaotic neural networks with known or unknown parameters

This paper is concerned with the synchronization problem for a class of stochastic neural networks with unknown parameters and mixed time-delays via output coupling. The mixed time-delays comprise the time-varying delay and distributed delay, and the neural networks are subjected to stochastic disturbances described in terms of a Brownian motion. Firstly, we use Lyapunov functions to establish general theoretical conditions for designing the output coupling matrix. Secondly, by using the adaptive feedback technique, a simple, analytical and rigorous approach is proposed to synchronize the stochastic neural networks with unknown parameters and mixed time-delays. Finally, numerical simulation results are given to show the effectiveness of the proposed method.

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Adaptive Synchronization of Fractional-Order Complex-Valued Chaotic Neural Networks with Time-Delay and Unknown Parameters

Physics ◽

10.3390/physics3040058 ◽

2021 ◽

Vol 3 (4) ◽

pp. 924-941

Author(s):

Mei Li ◽

Ruoxun Zhang ◽

Shiping Yang

Keyword(s):

Neural Networks ◽

Time Delay ◽

Fractional Order ◽

Adaptive Synchronization ◽

Order Complex ◽

Unknown Parameters ◽

Chaotic Neural Networks ◽

Controlled Systems ◽

The Stability ◽

Complex Valued

The purpose of this paper is to study and analyze the concept of fractional-order complex-valued chaotic networks with external bounded disturbances and uncertainties. The synchronization problem and parameter identification of fractional-order complex-valued chaotic neural networks (FOCVCNNs) with time-delay and unknown parameters are investigated. Synchronization between a driving FOCVCNN and a response FOCVCNN, as well as the identification of unknown parameters are implemented. Based on fractional complex-valued inequalities and stability theory of fractional-order chaotic complex-valued systems, the paper designs suitable adaptive controllers and complex update laws. Moreover, it scientifically estimates the uncertainties and external disturbances to establish the stability of controlled systems. The computer simulation results verify the correctness of the proposed method. Not only a new method for analyzing FOCVCNNs with time-delay and unknown complex parameters is provided, but also a sensitive decrease of the computational and analytical complexity.

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Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

Mathematical Problems in Engineering ◽

10.1155/2018/1603629 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 6

Author(s):

Bo Meng ◽

Xiaohong Wang

Keyword(s):

Neural Networks ◽

Fractional Order ◽

Sliding Mode ◽

Small Region ◽

Hopfield Neural Networks ◽

Adaptive Synchronization ◽

Unknown Parameters ◽

External Disturbances ◽

Lyapunov Stability Criterion ◽

Order Extension

Adaptive synchronization for a class of uncertain delayed fractional-order Hopfield neural networks (FOHNNs) with external disturbances is addressed in this paper. For the unknown parameters and external disturbances of the delayed FOHNNs, some adaptive estimations are designed. Firstly, a fractional-order switched sliding surface is proposed for the delayed FOHNNs. Then, according to the fractional-order extension of the Lyapunov stability criterion, a fractional-order sliding mode controller is constructed to guarantee that the synchronization error of the two uncertain delayed FOHNNs converges to an arbitrary small region of the origin. Finally, a numerical example of two-dimensional uncertain delayed FOHNNs is given to verify the effectiveness of the proposed method.

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Adaptive Synchronization in Unknown Stochastic Chaotic Neural Networks with Mixed Time-Varying Delays

Chaos Synchronization and Cryptography for Secure Communications - Advances in Information Security, Privacy, and Ethics ◽

10.4018/978-1-61520-737-4.ch013 ◽

2011 ◽

pp. 289-313

Author(s):

Jian-an Fang ◽

Yang Tang

Keyword(s):

Neural Networks ◽

Sufficient Conditions ◽

Stochastic Perturbation ◽

Adaptive Synchronization ◽

Output Coupling ◽

Time Varying ◽

Connection Weight ◽

Chaotic Neural Networks ◽

Simulation Results ◽

Feedback Techniques

Neural networks (NNs) have been useful in many fields, such as pattern recognition, image processing etc. Recently, synchronization of chaotic neural networks (CNNs) has drawn increasing attention due to the high security of neural networks. In this chapter, the problem of synchronization and parameter identification for a class of chaotic neural networks with stochastic perturbation via state and output coupling, which involve both the discrete and distributed time-varying delays has been investigated. Using adaptive feedback techniques, several sufficient conditions have been derived to ensure the synchronization of stochastic chaotic neural networks. Moreover, all the connection weight matrices can be estimated while the lag synchronization and complete synchronization is achieved in mean square at the same time. The corresponding simulation results are given to show the effectiveness of the proposed method.

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