Global synchronization in arrays of delayed neural networks with constant and delayed coupling

2006 ◽  
Vol 353 (4) ◽  
pp. 318-325 ◽  
Author(s):  
Jinde Cao ◽  
Ping Li ◽  
Weiwei Wang
Keyword(s):  
Neural Networks ◽  
Global Synchronization ◽  
Delayed Neural Networks ◽  
Delayed Coupling

GLOBAL SYNCHRONIZATION IN AN ARRAY OF LINEARLY COUPLED DELAYED NEURAL NETWORKS WITH AN ARBITRARY COUPLING MATRIX

2006 ◽  
Vol 16 (11) ◽  
pp. 3357-3368 ◽  
Author(s):  
HONGTAO LU ◽  
GUANRONG CHEN
Keyword(s):  
Neural Networks ◽  
Numerical Simulations ◽  
Output Coupling ◽  
Sufficient Condition ◽  
Global Synchronization ◽  
Coupling Matrix ◽  
Delayed Neural Networks ◽  
Arbitrary Coupling ◽  
General Sufficient Condition ◽  
Theoretical Results

In this paper, we investigate global synchronization in an array of linearly coupled identical delayed neural networks. We consider the array with an arbitrary coupling matrix without assuming it to be symmetric, irreducible and diffusive. Moreover, we consider the array being connected through two different coupling schemes, state-coupling and output-coupling, respectively. For state-coupling, we derive a more general sufficient condition ensuring global synchronization, which is an extension of some existing results in the literature. For output-coupling, we derive a new sufficient condition for global synchronization. Numerical simulations are given to illustrate the theoretical results.

GLOBAL SYNCHRONIZATION OF COUPLED DELAYED NEURAL NETWORKS AND APPLICATIONS TO CHAOTIC CNN MODELS

2004 ◽  
Vol 14 (07) ◽  
pp. 2229-2240 ◽  
Author(s):  
GUANRONG CHEN ◽  
JIN ZHOU ◽  
ZENGRONG LIU
Keyword(s):  
Neural Networks ◽  
Lyapunov Functional ◽  
Matrix Theory ◽  
Hermitian Matrix ◽  
Sufficient Condition ◽  
Global Synchronization ◽  
Coupling Matrix ◽  
Chaotic Neural Networks ◽  
Delayed Neural Networks ◽  
Functional Methods

This paper formulates the model and then studies its dynamics of a system of linearly and diffusively coupled identical delayed neural networks (DNNs), which is generalization of delayed Hopfied neural networks (DHNNs) and delayed cellular neural networks (DCNNs). In particularly, a simple yet generic sufficient condition for global synchronization of such coupled DNNs is derived based on the Lyapunov functional methods and Hermitian matrix theory. It is shown that global synchronization of coupled DNNs is ensured by a suitable design of the coupling matrix and the inner linking matrix. Furthermore, the result is applied to some typical chaotic neural networks. Finally, numerical simulations are presented to demonstrate the effectiveness of the approach.

Adaptive state estimation of Markov switched neural networks driven by Lévy noise

2019 ◽  
Vol 42 (2) ◽  
pp. 330-336
Author(s):  
Dongbing Tong ◽  
Qiaoyu Chen ◽  
Wuneng Zhou ◽  
Yuhua Xu
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Lévy Noise ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Switched Neural Networks ◽  
Inequality Technique ◽  
Levy Noise

This paper proposes the [Formula: see text]-matrix method to achieve state estimation in Markov switched neural networks with Lévy noise, and the method is very distinct from the linear matrix inequality technique. Meanwhile, in light of the Lyapunov stability theory, some sufficient conditions of the exponential stability are derived for delayed neural networks, and the adaptive update law is obtained. An example verifies the condition of state estimation and confirms the effectiveness of results.

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