scholarly journals Global Convergence for Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yanyan Wang ◽  
Jianping Zhou
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Contraction Mapping ◽  
Contraction Mapping Principle ◽  
Activation Functions ◽  
Discontinuous Activation ◽  
Globally Exponential Stability ◽  
Discontinuous Activation Functions

Cohen-Grossberg neural networks with discontinuous activation functions is considered. Using the property ofM-matrix and a generalized Lyapunov-like approach, the uniqueness is proved for state solutions and corresponding output solutions, and equilibrium point and corresponding output equilibrium point of considered neural networks. Meanwhile, global exponential stability of equilibrium point is obtained. Furthermore, by contraction mapping principle, the uniqueness and globally exponential stability of limit cycle are given. Finally, an example is given to illustrate the effectiveness of the obtained results.

Global exponential stability of periodic solution of delayed discontinuous Cohen–Grossberg neural networks and its applications

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Yiyuan Chai ◽  
Jiqiang Feng ◽  
Sitian Qin ◽  
Xinyu Pan
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Activation Functions ◽  
Functional Theory ◽  
Alternative Theorem ◽  
Discontinuous Activation ◽  
Inclusion Theory ◽  
Discontinuous Activation Functions

Abstract This paper is concerned with the existence and global exponential stability of the periodic solution of delayed Cohen–Grossberg neural networks (CGNNs) with discontinuous activation functions. The activations considered herein are non-decreasing but not required to be Lipschitz or continuous. Based on differential inclusion theory, Lyapunov functional theory and Leary–Schauder alternative theorem, some sufficient criteria are derived to ensure the existence and global exponential stability of the periodic solution. In order to show the superiority of the obtained results, an application and some detailed comparisons between some existing related results and our results are presented. Finally, some numerical examples are also illustrated.

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.

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.

GLOBAL EXPONENTIAL STABILITY OF FUZZY INTERVAL DELAYED NEURAL NETWORKS WITH IMPULSES ON TIME SCALES

2009 ◽  
Vol 19 (06) ◽  
pp. 449-456 ◽  
Author(s):  
YONGKUN LI ◽  
TIANWEI ZHANG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Time Scales ◽  
Global Exponential Stability ◽  
Lyapunov Method ◽  
Delayed Neural Networks ◽  
The Neural Networks ◽  
Uniqueness Of Equilibrium ◽  
Fuzzy Interval

In this paper, we investigate the existence and uniqueness of equilibrium point for fuzzy interval delayed neural networks with impulses on time scales. And we give the criteria of the global exponential stability of the unique equilibrium point for the neural networks under consideration using Lyapunov method. Finally, we present an example to illustrate that our results are effective.

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