scholarly journals Existence and Exponential Stability of Solutions for Stochastic Cellular Neural Networks with Piecewise Constant Argument

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaoai Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Inequality Technique ◽  
Generalized Type ◽  
Moment Exponential Stability ◽  
Constant Argument

By using the concept of differential equations with piecewise constant argument of generalized type, a model of stochastic cellular neural networks with piecewise constant argument is developed. Sufficient conditions are obtained for the existence and uniqueness of the equilibrium point for the addressed neural networks.pth moment exponential stability is investigated by means of Lyapunov functional, stochastic analysis, and inequality technique. The results in this paper improve and generalize some of the previous ones. An example with numerical simulations is given to illustrate our results.

Global Exponential Stability of Cohen-Grossberg Neural Networks with Piecewise Constant Argument of Generalized Type and Impulses

2016 ◽  
Vol 28 (1) ◽  
pp. 229-255 ◽  
Author(s):  
Qiang Xi
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Lyapunov Function Method ◽  
Generalized Type ◽  
Constant Argument

In this letter, we consider a model of Cohen-Grossberg neural networks with piecewise constant argument of generalized type and impulses. Sufficient conditions ensuring the existence and uniqueness of solutions are obtained. Based on constructing a new differential inequality with piecewise constant argument and impulse and using the Lyapunov function method, we derive sufficient conditions ensuring the global exponential stability of equilibrium point, with approximate exponential convergence rate. An example is given to illustrate the validity and advantage of the theoretical results.

scholarly journals Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays

2011 ◽  
Vol 21 (4) ◽  
pp. 649-658 ◽  
Author(s):  
Qianhong Zhang ◽  
Lihui Yang ◽  
Daixi Liao
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Exponential Stability ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique

Existence and exponential stability of a periodic solution for fuzzy cellular neural networks with time-varying delays Fuzzy cellular neural networks with time-varying delays are considered. Some sufficient conditions for the existence and exponential stability of periodic solutions are obtained by using the continuation theorem based on the coincidence degree and the differential inequality technique. The sufficient conditions are easy to use in pattern recognition and automatic control. Finally, an example is given to show the feasibility and effectiveness of our methods.

EXPONENTIAL p-STABILITY OF STOCHASTIC REACTION–DIFFUSION CELLULAR NEURAL NETWORKS WITH MULTIPLE DELAYS

2009 ◽  
Vol 19 (10) ◽  
pp. 3373-3386 ◽  
Author(s):  
RANCHAO WU
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Matrix Analysis ◽  
Multiple Delays ◽  
Space Matrix ◽  
Stochastic Reaction ◽  
Moment Exponential Stability

In the current paper, a class of stochastic cellular neural networks with reaction–diffusion effects, both discrete and distributed time delays, is studied. Several sufficient conditions guaranteeing the almost sure and pth moment exponential stability of its equilibrium solution are respectively obtained through analytic methods such as employing Lyapunov functional, applying Itô's formula, inequality techniques, embedding in Banach space, Matrix analysis and semimartingale convergence theorem. The yielded conclusions, which are independent of diffusion terms and delays, assume much less restrictions on activation functions and interconnection weights, and can be applied within a broader range of neural networks. Moreover, through the obtained results, it could be noted that noise will affect the exponential stability of the system. For illustration, two examples are given to show the feasibility of results.

GLOBAL EXPONENTIAL STABILITY OF IMPULSIVE FUZZY CELLULAR NEURAL NETWORKS WITH DELAYS AND DIFFUSION

2009 ◽  
Vol 19 (01) ◽  
pp. 245-261 ◽  
Author(s):  
KELIN LI
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Mixed Delays ◽  
Fuzzy Cellular Neural Networks ◽  
Inequality Technique ◽  
And Diffusion

In this paper, a class of impulsive fuzzy cellular neural networks (FCNNs) with mixed delays and diffusion is formulated and investigated. By establishing an intergro-differential inequality, applying M-matrix theory and inequality technique, several sufficient conditions are obtained to ensure the existence, uniqueness and global exponential stability of an equilibrium point for impulsive FCNNs with mixed delays and diffusion. In particular, the estimate of the exponential convergence rate is also provided, which depends on the system parameters and impulses. These results generalize and improve the earlier publications. Some examples are given to show the effectiveness of the obtained results. It is believed that these results are significant and useful for the design and applications of FCNNs.

Sign in / Sign up

Export Citation Format

Share Document