Exponential Stability of Stochastic Reaction-Diffusion Neural Networks with Mixed Delays in Procurement of Maintenance Material

2011 ◽  
Vol 105-107 ◽  
pp. 2315-2320
Author(s):  
Xiao Chen
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Exponential Stability ◽  
Effective Means ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Mixed Delays ◽  
The Neural Network ◽  
Discrete Time Delay

In order to effectively improve the equipment maintenance material procurement management efficiency, improve economic efficiency of using the procurement funds, strengthen mathematical theory applications in the area of procurement, the neural network used in evaluation of organizational change is one of the most effective means. In this paper, a class of stochastic Cohen–Grossberg neural networks with reaction-diffusion terms, discrete time delay and distributed time delay is investigated. First, we describe the modeling, illuminate the significance of the system and introduce some preliminary definitions and lemmas which will be employed throughout the paper. Then, by using the Lyapunov functional method, M-matrix properties, nonnegative semimartingale convergence theorem and some inequality technique, sufficient conditions are obtained to guarantee the exponential stability of the system.

scholarly journals Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Chuangxia Huang ◽  
Xinsong Yang ◽  
Yigang He ◽  
Lehua Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Distributed Delays ◽  
Almost Sure Exponential Stability ◽  
Mean Square Exponential Stability ◽  
Stochastic Reaction

Stability of reaction-diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some new sufficient conditions to guarantee the almost sure exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov's functional method, M-matrix properties, some inequality technique, and nonnegative semimartingale convergence theorem are used in our approach. The obtained conclusions improve some published results.

scholarly journals Global Robust Exponential Stability and Periodic Solutions for Interval Cohen-Grossberg Neural Networks with Mixed Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Yanke Du ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Complex Dynamics ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Robust Exponential Stability ◽  
Global Robust Exponential Stability

A class of interval Cohen-Grossberg neural networks with time-varying delays and infinite distributed delays is investigated. By employing H-matrix and M-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions are established for the existence, uniqueness, and global robust exponential stability of the equilibrium point and the periodic solution to the neural networks. Our results improve some previously published ones. Finally, numerical examples are given to illustrate the feasibility of the theoretical results and further to exhibit that there is a characteristic sequence of bifurcations leading to a chaotic dynamics, which implies that the system admits rich and complex dynamics.

scholarly journals Global Robust Exponential Stability Analysis for Interval Neural Networks with Mixed Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Yanke Du ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Robust Exponential Stability ◽  
Interval Neural Networks ◽  
Global Robust Exponential Stability

A class of interval neural networks with time-varying delays and distributed delays is investigated. By employingH-matrix andM-matrix theory, homeomorphism techniques, Lyapunov functional method, and linear matrix inequality approach, sufficient conditions for the existence, uniqueness, and global robust exponential stability of the equilibrium point to the neural networks are established and some previously published results are improved and generalized. Finally, some numerical examples are given to illustrate the effectiveness of the theoretical results.

scholarly journals A perspective on graph theory-based stability analysis of impulsive stochastic recurrent neural networks with time-varying delays

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
M. Iswarya ◽  
R. Raja ◽  
G. Rajchakit ◽  
J. Cao ◽  
J. Alzabut ◽  
...  
Keyword(s):  
Neural Networks ◽  
Graph Theory ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Lyapunov Functional ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Theoretic Approach ◽  
Discrete Time Delay

AbstractIn this work, the exponential stability problem of impulsive recurrent neural networks is investigated; discrete time delay, continuously distributed delay and stochastic noise are simultaneously taken into consideration. In order to guarantee the exponential stability of our considered recurrent neural networks, two distinct types of sufficient conditions are derived on the basis of the Lyapunov functional and coefficient of our given system and also to construct a Lyapunov function for a large scale system a novel graph-theoretic approach is considered, which is derived by utilizing the Lyapunov functional as well as graph theory. In this approach a global Lyapunov functional is constructed which is more related to the topological structure of the given system. We present a numerical example and simulation figures to show the effectiveness of our proposed work.

scholarly journals Exponential Stability and Periodicity of Fuzzy Delayed Reaction-Diffusion Cellular Neural Networks with Impulsive Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guowei Yang ◽  
Yonggui Kao ◽  
Changhong Wang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Impulsive Effect ◽  
Time Varying ◽  
Delayed Reaction

This paper considers dynamical behaviors of a class of fuzzy impulsive reaction-diffusion delayed cellular neural networks (FIRDDCNNs) with time-varying periodic self-inhibitions, interconnection weights, and inputs. By using delay differential inequality,M-matrix theory, and analytic methods, some new sufficient conditions ensuring global exponential stability of the periodic FIRDDCNN model with Neumann boundary conditions are established, and the exponential convergence rate index is estimated. The differentiability of the time-varying delays is not needed. An example is presented to demonstrate the efficiency and effectiveness of the obtained results.

scholarly journals Synchronization of Discrete-Time Stochastic Neural Networks with Random Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Haibo Bao ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Stochastic Neural Networks ◽  
Time Varying Delay ◽  
Random Delays ◽  
Random Fashion ◽  
Analysis Technique

By using a Lyapunov-Krasovskii functional method and the stochastic analysis technique, we investigate the problem of synchronization for discrete-time stochastic neural networks (DSNNs) with random delays. A control law is designed, and sufficient conditions are established that guarantee the synchronization of two identical DSNNs with random delays. Compared with the previous works, the time delay is assumed to be existent in a random fashion. The stochastic disturbances are described in terms of a Brownian motion and the time-varying delay is characterized by introducing a Bernoulli stochastic variable. Two examples are given to illustrate the effectiveness of the proposed results. The main contribution of this paper is that the obtained results are dependent on not only the bound but also the distribution probability of the time delay. Moreover, our results provide a larger allowance variation range of the delay, and are less conservative than the traditional delay-independent ones.

scholarly journals Exponential Stabilization of Coupled Hybrid Stochastic Delayed BAM Neural Networks: A Periodically Intermittent Control Method

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Yunjian Peng ◽  
Birong Zhao ◽  
Weijie Sun ◽  
Feiqi Deng
Keyword(s):  
Neural Networks ◽  
Closed Loop ◽  
Control Method ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Exponential Stabilization ◽  
Intermittent Control ◽  
Analysis Techniques ◽  
Basic Parameters

This paper considers exponential stabilization for a class of coupled hybrid stochastic delayed bidirectional associative memory neural networks (HSD-BAM-NN) with reaction-diffusion terms. A periodically intermittent controller is proposed to exponentially stabilize such an unstable HSD-BAM-NN, and sufficient conditions of the closed-loop BAM-NN system with exponential stabilization are derived by using Lyapunov-Krasovskii functional method, stochastic analysis techniques, and integral inequality property, which decide the basic parameters of the proposed controller. Furthermore, a framework to establish simulation algorithm with sampled states is presented to implement the stabilization controller. With a HSD-BAM-NN model of power synchronization in a photovoltaic (PV) array field, we illustrate numerical simulation results to verify the correctness and effectiveness of the proposed controller.

GLOBAL EXPONENTIAL STABILITY AND PERIODIC OSCILLATIONS OF REACTION–DIFFUSION BAM NEURAL NETWORKS WITH PERIODIC COEFFICIENTS AND GENERAL DELAYS

2007 ◽  
Vol 17 (01) ◽  
pp. 129-142 ◽  
Author(s):  
QINGHUA ZHOU ◽  
JIANHUA SUN ◽  
GUANRONG CHEN
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Activation Functions ◽  
Bidirectional Associative Memory ◽  
Connection Weight ◽  
Periodic Coefficients ◽  
Delay Dependent

For a large class of reaction–diffusion bidirectional associative memory (RDBAM) neural networks with periodic coefficients and general delays, several new delay-dependent or delay-independent sufficient conditions ensuring the existence and global exponential stability of a unique periodic solution are given, by constructing suitable Lyapunov functionals and employing some analytic techniques such as Poincaré mapping. The presented conditions are easily verifiable and useful in the design and applications of RDBAM neural networks. Moreover, the employed analytic techniques do not require the symmetry of the bidirectional connection weight matrix, the boundedness, monotonicity and differentiability of activation functions of the network. In several ways, the results generalize and improve those established in the current literature.

scholarly journals Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-20 ◽  
Author(s):  
Xiaohui Xu ◽  
Jibin Yang ◽  
Yanhai Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Mixed Delays ◽  
Mean Square ◽  
Integral Theorem ◽  
Stochastic Disturbance ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
Complex Valued

This paper investigates the mean square exponential stability problem of a class of complex-valued neural networks with stochastic disturbance and mixed delays including both time-varying delays and continuously distributed delays. Under different assumption conditions concerning stochastic disturbance term from the existing ones, some sufficient conditions are derived for assuring the mean square exponential stability of the equilibrium point of the system based on the vector Lyapunov function method and Ito^ differential-integral theorem. The obtained results not only generalize the existing ones, but also reduce the conservatism of the previous stability results about complex-valued neural networks with stochastic disturbances. Two numerical examples with simulation results are given to verify the feasibility of the proposed results.

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