Generating Globally Stable Periodic Solutions of Delayed Neural Networks With Periodic Coefficients via Impulsive Control

A general methodology that involves geometric configuration of the network structure for studying multistability and multiperiodicity is developed. We consider a general class of nonautonomous neural networks with delays and various activation functions. A geometrical formulation that leads to a decomposition of the phase space into invariant regions is employed. We further derive criteria under which the n-neuron network admits 2n exponentially stable sets. In addition, we establish the existence of 2n exponentially stable almost periodic solutions for the system, when the connection strengths, time lags, and external bias are almost periodic functions of time, through applying the contraction mapping principle. Finally, three numerical simulations are presented to illustrate our theory.

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Synchronization of Chaotic Delayed Neural Networks via Impulsive Control

Journal of Applied Mathematics ◽

10.1155/2014/305264 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Yang Fang ◽

Kang Yan ◽

Kelin Li

Keyword(s):

Neural Networks ◽

Impulsive Control ◽

Sufficient Conditions ◽

Stability Theorem ◽

Linear Matrix ◽

Matrix Inequality ◽

Lyapunov Stability Theorem ◽

Delayed Neural Networks ◽

Impulsive Synchronization ◽

Synchronization Problem

This paper is concerned with the impulsive synchronization problem of chaotic delayed neural networks. By employing Lyapunov stability theorem, impulsive control theory and linear matrix inequality (LMI) technique, several new sufficient conditions ensuring the asymptotically synchronization for coupled chaotic delayed neural networks are derived. Based on these new sufficient conditions, an impulsive controller is designed. Moreover, the stable impulsive interval of synchronized neural networks is objectively estimated by combining the MATLAB LMI toolbox and one of the two given equations. Two examples with numerical simulations are given to illustrate the effectiveness of the proposed method.

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Synchronization of delayed neural networks with hybrid coupling via impulsive control

Transactions of the Institute of Measurement and Control ◽

10.1177/0142331219834993 ◽

2019 ◽

Vol 41 (13) ◽

pp. 3714-3724 ◽

Cited By ~ 1

Author(s):

Tianhu Yu ◽

Huamin Wang ◽

Dengqing Cao

Keyword(s):

Neural Networks ◽

Linear Matrix Inequalities ◽

Upper Bound ◽

Hybrid Control ◽

Impulsive Control ◽

Distributed Delay ◽

Linear Matrix ◽

Matrix Inequalities ◽

Delayed Neural Networks ◽

Coupled Neural Networks

The synchronization problem of coupled neural networks via impulsive control is investigated in the present paper. Based on a time varying Lyapunov functional associated with the impulsive time sequence, the delay-dependent criteria in terms of linear matrix inequalities are derived to guarantee the synchronization of the coupled neural networks. The obtained criteria are closely related to both the lower and the upper bound of the adjacent impulsive instant difference. By solving the corresponding linear matrix inequalities, the synchronization criteria can be used to estimate the upper bound of both transmission delay and distributed-delay. The low-dimensional criteria also are obtained for the coupled neural networks with identical nodes. Finally, two examples are given to illustrate the validity of the proposed hybrid control.

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