scholarly journals Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaohui Xu ◽  
Jiye Zhang ◽  
Quan Xu ◽  
Zilong Chen ◽  
Weifan Zheng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Time Varying ◽  
Homeomorphism Mapping ◽  
Complex Valued

This paper studies the global exponential stability for a class of impulsive disturbance complex-valued Cohen-Grossberg neural networks with both time-varying delays and continuously distributed delays. Firstly, the existence and uniqueness of the equilibrium point of the system are analyzed by using the corresponding property of M-matrix and the theorem of homeomorphism mapping. Secondly, the global exponential stability of the equilibrium point of the system is studied by applying the vector Lyapunov function method and the mathematical induction method. The established sufficient conditions show the effects of both delays and impulsive strength on the exponential convergence rate. The obtained results in this paper are with a lower level of conservatism in comparison with some existing ones. Finally, three numerical examples with simulation results are given to illustrate the correctness of the proposed results.

GLOBAL EXPONENTIAL STABILITY OF CHUA'S REACTION–DIFFUSION CNN

2009 ◽  
Vol 19 (10) ◽  
pp. 3397-3406
Author(s):  
YUNQUAN KE ◽  
CHUNFANG MIAO
Keyword(s):  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Analytical Techniques ◽  
Reaction Diffusion ◽  
Coefficient Matrix ◽  
Homeomorphism Mapping

In this paper, the global exponential stability of Chua's reaction–diffusion CNN system is investigated. For this system, some sufficient conditions ensuring the existence and global exponential stability of the equilibrium point is derived by using homeomorphism mapping, the property of coefficient matrix and analytical techniques. Finally, three illustrative examples are given to show the effectiveness of our results.

ATTRACTABILITY AND LOCATION OF EQUILIBRIUM POINT OF CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

2004 ◽  
Vol 14 (05) ◽  
pp. 337-345 ◽  
Author(s):  
ZHIGANG ZENG ◽  
DE-SHUANG HUANG ◽  
ZENGFU WANG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Cellular Neural Networks ◽  
Stability Conditions ◽  
Time Varying ◽  
The Stability ◽  
Theoretical Results

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be obtained. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

EXPONENTIAL STABILITY ANALYSIS OF NEURAL NETWORKS WITH VARIABLE DELAYS

2010 ◽  
Vol 20 (05) ◽  
pp. 1541-1549 ◽  
Author(s):  
MAN-CHUN TAN ◽  
YAN ZHANG ◽  
WEN-LI SU ◽  
YU-NONG ZHANG
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Variable Delays

Some sufficient conditions to ensure the existence, uniqueness and global exponential stability of the equilibrium point of cellular neural networks with variable delays are derived. These results extend and improve the existing ones in the literature. Two illustrative examples are given to demonstrate the effectiveness of our results.

scholarly journals Existence and Exponential Stability of Equilibrium Point for Fuzzy BAM Neural Networks with Infinitely Distributed Delays and Impulses on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Yongkun Li ◽  
Lijie Sun ◽  
Li Yang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Bam Neural Networks ◽  
Stability Of Equilibrium ◽  
Fuzzy Bam Neural Networks ◽  
The Fixed Point Theorem

By using the fixed point theorem and constructing a Lyapunov functional, we establish some sufficient conditions on the existence, uniqueness, and exponential stability of equilibrium point for a class of fuzzy BAM neural networks with infinitely distributed delays and impulses on time scales. We also present a numerical example to show the feasibility of obtained results. Our example also shows that the described time and continuous neural time networks have the same dynamic behaviours for the stability.

scholarly journals Periodic Solutions of a Cohen-Grossberg-Type BAM Neural Networks with Distributed Delays and Impulses

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Qiming Liu ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Bam Neural Networks ◽  
Mathematical Transformation

A class of Cohen-Grossberg-type BAM neural networks with distributed delays and impulses are investigated in this paper. Sufficient conditions to guarantee the uniqueness and global exponential stability of the periodic solutions of such networks are established by using suitable Lyapunov function, the properties ofM-matrix, and some suitable mathematical transformation. The results in this paper improve the earlier publications.

scholarly journals Impulsive Cohen-Grossberg neural networks with s-type distributed delays

2011 ◽  
Vol 48 (1) ◽  
pp. 1-13
Author(s):  
Haydar Akça ◽  
Valéry Covachev
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Unique Equilibrium ◽  
Analysis Techniques

Abstract We study impulsive Cohen-Grossberg neural networks with S-type distributed delays. This type of delays in the presence of impulses is more general than the usual types of delays studied in the literature. Using analysis techniques we prove the existence of a unique equilibrium point. By means of simple and efficient Lyapunov functions we present some sufficient conditions for the exponential stability of the equilibrium.

scholarly journals Exponential Stability for Discrete-Time Stochastic BAM Neural Networks with Discrete and Distributed Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-23
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Bam Neural Networks ◽  
Analysis Problem ◽  
The Stability

This paper deals with the stability analysis problem for a class of discrete-time stochastic BAM neural networks with discrete and distributed time-varying delays. By constructing a suitable Lyapunov-Krasovskii functional and employing M-matrix theory, we find some sufficient conditions ensuring the global exponential stability of the equilibrium point for stochastic BAM neural networks with time-varying delays. The conditions obtained here are expressed in terms of LMIs whose feasibility can be easily checked by MATLAB LMI Control toolbox. A numerical example is presented to show the effectiveness of the derived LMI-based stability conditions.

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