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 Dynamics of Fuzzy BAM Neural Networks with Distributed Delays and Diffusion

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Jingzhong Liu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Oscillatory Solution ◽  
Distributed Delays ◽  
Bam Neural Networks ◽  
Fuzzy Bam Neural Networks ◽  
Inequality Technique ◽  
And Diffusion

Constructing a new Lyapunov functional and employing inequality technique, the existence, uniqueness, and global exponential stability of the periodic oscillatory solution are investigated for a class of fuzzy bidirectional associative memory (BAM) neural networks with distributed delays and diffusion. We obtained some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the periodic solution. The results remove the usual assumption that the activation functions are differentiable. An example is provided to show the effectiveness of our results.

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.

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.

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