scholarly journals Exponential Stability of Periodic Solutions for Inertial Type BAM Cohen-Grossberg Neural Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-19 ◽  
Author(s):  
Chunfang Miao ◽  
Yunquan Ke
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Mean Value ◽  
Mean Value Theorem ◽  
First Order ◽  
Inequality Technique ◽  
Variable Substitution ◽  
Differential Mean Value Theorem

The existence and exponential stability of periodic solutions for inertial type BAM Cohen-Grossberg neural networks are investigated. First, by properly choosing variable substitution, the system is transformed to first order differential equation. Second, some sufficient conditions that ensure the existence and exponential stability of periodic solutions for the system are obtained by constructing suitable Lyapunov functional and using differential mean value theorem and inequality technique. Finally, two examples are given to illustrate the effectiveness of the results.

scholarly journals Global exponential stability and existence of periodic solutions of fuzzy wave equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Wei Liu ◽  
Yimin Lou
Keyword(s):  
Periodic Solution ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Global Exponential Stability ◽  
Wave Equations ◽  
Sufficient Conditions ◽  
First Order ◽  
Variable Substitution ◽  
Existence Of Periodic Solutions

AbstractIn this paper, the global exponential stability and the existence of periodic solutions of fuzzy wave equations are investigated. By variable substitution the system of partial differential equations (PDEs) is transformed from second order to first order. Some sufficient conditions that ensure the global exponential stability and the existence of periodic solution of the system are obtained by an analysis that uses a suitable Lyapunov functional. In addition, a concrete example is given to show the effectiveness of the results.

GLOBAL EXPONENTIAL STABILITY OF HIGH-ORDER BAM NEURAL NETWORKS WITH REACTION–DIFFUSION TERMS

2010 ◽  
Vol 20 (10) ◽  
pp. 3209-3223 ◽  
Author(s):  
FENG-YAN ZHOU ◽  
CHENG-RONG MA
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Time Delays ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Mean Value ◽  
High Order ◽  
Mean Value Theorem ◽  
Bam Neural Networks

The global exponential stability is studied for a class of high-order bi-directional associative memory (BAM) neural networks with time delays and reaction–diffusion terms. By constructing suitable Lyapunov functional, using differential mean value theorem and homeomorphism, several sufficient conditions guaranteeing the existence, uniqueness and global exponential stability of high-order BAM neural networks with time delays and reaction–diffusion terms are given. Two illustrative examples are also given in the end to show the effectiveness of our 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.

scholarly journals The Existence and Global Exponential Stability of Almost Periodic Solutions for Neutral-Type CNNs on Time Scales

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 321 ◽  
Author(s):  
Bing Li ◽  
Yongkun Li ◽  
Xiaofang Meng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Global Exponential Stability ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays

In this paper, neutral-type competitive neural networks with mixed time-varying delays and leakage delays on time scales are proposed. Based on the contraction fixed-point theorem, some sufficient conditions that are independent of the backwards graininess function of the time scale are obtained for the existence and global exponential stability of almost periodic solutions of neural networks under consideration. The results obtained are brand new, indicating that the continuous time and discrete-time conditions of the network share the same dynamic behavior. Finally, two examples are given to illustrate the validity of the results obtained.

The anti-periodic oscillations of shunting inhibitory cellular neural networks with time-varying delays and continuously distributed delays

2017 ◽  
Vol 10 (4) ◽  
pp. 513-529
Author(s):  
Changjin Xu ◽  
Peiluan Li
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Cellular Neural Networks ◽  
Distributed Delays ◽  
Time Varying ◽  
Content Type ◽  
All Solutions ◽  
Inequality Technique

Purpose The purpose of this paper is to study the existence and exponential stability of anti-periodic solutions of a class of shunting inhibitory cellular neural networks (SICNNs) with time-varying delays and continuously distributed delays. Design/methodology/approach The inequality technique and Lyapunov functional method are applied. Findings Sufficient conditions are obtained to ensure that all solutions of the networks converge exponentially to the anti-periodic solution, which are new and complement previously known results. Originality/value There are few papers that deal with the anti-periodic solutions of delayed SICNNs with the form negative feedback – aij(t)αij(xij(t)).

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.

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.

Exponential stability of anti-periodic solutions for neural networks with multiple discrete and distributed delays

2008 ◽  
Vol 223 (3) ◽  
pp. 299-308 ◽  
Author(s):  
X Liu ◽  
J Cao
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Matrix Theory ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Distributed Delays ◽  
Generalized Neural Networks ◽  
Discrete Delays ◽  
Analysis Of Stability

In this paper, the anti-periodic solutions are considered for generalized neural networks with multiple discrete delays and distributed delays. Several new sufficient conditions are established for ensuring the existence and exponential stability of anti-periodic solutions based on the Lyapunov method and M-matrix theory. It is shown that, by means of the techniques developed, the analysis of stability for anti-periodic solutions is different from the familiar periodic ones. The obtained results generalize and improve the earlier works. Two numerical examples are given to illustrate the effectiveness of the proposed theories.

Existence and Global Exponential Stability of Almost Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Distributed Leakage Delays on Time Scales

2016 ◽  
Vol 13 (10) ◽  
pp. 7054-7065
Author(s):  
Changjin Xu ◽  
Xiaofei Li ◽  
Songbo Hu ◽  
Haitao Wu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Time Scales ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Linear Differential

In this paper, we deal with a class of shunting inhibitory cellular neural networks (SICNNs) with distributed leakage delays on time scales. Some sufficient conditions which ensure the existence and exponential stability of almost periodic solutions for such class of SICNNs are obtained by applying the exponential dichotomy of linear differential equations, Lapunov functional method and contraction mapping principle. An example is given to illustrate the effectiveness of the theoretical results. The results obtained in this paper are completely new and complement the previously known studies.

scholarly journals Periodic Solutions for a Numerical Discretization Neural Network

2010 ◽  
Vol 2010 ◽  
pp. 1-17
Author(s):  
Chun Lu
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Periodic Solutions ◽  
Global Exponential Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Numerical Discretization

The existence and global exponential stability of periodic solutions for a class of numerical discretization neural networks are considered. Using coincidence degree theory and Lyapunov method, sufficient conditions for the existence and global exponential stability of periodic solutions are obtained. Numerical simulations are given to illustrate the results.

Sign in / Sign up

Export Citation Format

Share Document