Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses

2013 ◽  
Vol 217 ◽  
pp. 62-79 ◽  
Author(s):  
Yongkun Li ◽  
Chao Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Bam Neural Networks ◽  
Stability Of Equilibrium ◽  
Variable Delays ◽  
Fuzzy Bam Neural Networks

scholarly journals Stochastic Dynamics of Discrete-Time Fuzzy Random BAM Neural Networks with Time Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Sufang Han ◽  
Tianwei Zhang ◽  
Guoxin Liu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Periodic Sequence ◽  
Stochastic Neural Networks ◽  
Bam Neural Networks ◽  
Almost Periodic ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Fuzzy Bam Neural Networks

By using the semidiscrete method of differential equations, a new version of discrete analogue of stochastic fuzzy BAM neural networks was formulated, which gives a more accurate characterization for continuous-time stochastic neural networks than that by the Euler scheme. Firstly, the existence of the 2p-th mean almost periodic sequence solution of the discrete-time stochastic fuzzy BAM neural networks is investigated with the help of Minkowski inequality, Hölder inequality, and Krasnoselskii’s fixed point theorem. Secondly, the 2p-th moment global exponential stability of the discrete-time stochastic fuzzy BAM neural networks is also studied by using some analytical skills in stochastic theory. Finally, two examples with computer simulations are given to demonstrate that our results are feasible. The main results obtained in this paper are completely new, and the methods used in this paper provide a possible technique to study 2p-th mean almost periodic sequence solution and 2p-th moment global exponential stability of semidiscrete stochastic fuzzy models.

A NOVEL GLOBAL EXPONENTIAL STABILITY RESULT FOR DISCRETE-TIME CELLULAR NEURAL NETWORKS WITH VARIABLE DELAYS

2006 ◽  
Vol 16 (06) ◽  
pp. 467-472 ◽  
Author(s):  
QIANG ZHANG ◽  
XIAOPENG WEI ◽  
JIN XU
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Stability Condition ◽  
Global Exponential Stability ◽  
Stability Result ◽  
Cellular Neural Networks ◽  
Unique Equilibrium ◽  
Variable Delays

Global exponential stability is considered for a class of discrete-time cellular neural networks with variable delays. By employing a discrete Halanay inequality, a new result is presented ensuring global exponential stability of the unique equilibrium point of the networks. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the delay. An example is given to illustrate the effectiveness of the global exponential stability condition provided here.

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 On Global Exponential Stability of Discrete-Time Hopfield Neural Networks with Variable Delays

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Qiang Zhang ◽  
Xiaopeng Wei ◽  
Jin Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Discrete Time ◽  
Global Exponential Stability ◽  
Stability Result ◽  
Hopfield Neural Networks ◽  
Difference Inequality ◽  
Variable Delays

Global exponential stability of a class of discrete-time Hopfield neural networks with variable delays is considered. By making use of a difference inequality, a new global exponential stability result is provided. The result only requires the delay to be bounded. For this reason, the result is milder than those presented in the earlier references. Furthermore, two examples are given to show the efficiency of our result.

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