scholarly journals Stability Analysis for Impulsive Stochastic Reaction-Diffusion Differential System and Its Application to Neural Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yanke Du ◽  
Yanlu Li ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Differential System ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Impulsive Effects ◽  
Stability Criteria ◽  
Mixed Time Delays ◽  
The Stability ◽  
Stochastic Reaction

This paper is concerned with the stability of impulsive stochastic reaction-diffusion differential systems with mixed time delays. First, an equivalent relation between the solution of a stochastic reaction-diffusion differential system with time delays and impulsive effects and that of corresponding system without impulses is established. Then, some stability criteria for the stochastic reaction-diffusion differential system with time delays and impulsive effects are derived. Finally, the stability criteria are applied to impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks with mixed time delays, and sufficient conditions are obtained for the exponentialp-stability of the zero solution to the neural networks. An example is given to illustrate the effectiveness of our theoretical results. The systems we studied in this paper are more general, and some existing results are improved and extended.

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

2010 ◽  
Vol 88 (12) ◽  
pp. 885-898 ◽  
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Time Delays ◽  
The Stability

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

scholarly journals Dynamical Behaviors of Impulsive Stochastic Reaction-Diffusion Neural Networks with Mixed Time Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Weiyuan Zhang ◽  
Junmin Li ◽  
Minglai Chen
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
Mixed Time Delays ◽  
Dynamical Behaviors ◽  
Proposed Model ◽  
The Mean ◽  
Stochastic Reaction

We discuss the dynamical behaviors of impulsive stochastic reaction-diffusion neural networks (ISRDNNs) with mixed time delays. By using a well-knownL-operator differential inequality with mixed time delays and combining with the Lyapunov-Krasovkii functional approach, as well as linear matrix inequality (LMI) technique, some novel sufficient conditions are derived to ensure the existence, uniqueness, and global exponential stability of the periodic solutions for ISRDNNs with mixed time delays in the mean square sense. The obtained sufficient conditions depend on the reaction-diffusion terms. The results of this paper are new and improve some of the previously known results. The proposed model is quite general since many factors such as noise perturbations, impulsive phenomena, and mixed time delays are considered. Finally, two numerical examples are provided to verify the usefulness of the obtained results.

MEAN VALUE EXPONENTIAL STABILITY OF STOCHASTIC REACTION–DIFFUSION GENERALIZED COHEN–GROSSBERG NEURAL NETWORKS WITH TIME-VARYING DELAY

2007 ◽  
Vol 17 (09) ◽  
pp. 3219-3227 ◽  
Author(s):  
LI WAN ◽  
QINGHUA ZHOU ◽  
JIANHUA SUN
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Mean Value ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Stability ◽  
Stochastic Reaction ◽  
Varying Delay

Stochastic effects on the stability property of reaction–diffusion generalized Cohen–Grossberg neural networks (GDCGNNs) with time-varying delay are considered. By skillfully constructing suitable Lyapunov functionals and employing the method of variational parameters, inequality technique and stochastic analysis, the delay independent and easily verifiable sufficient conditions to guarantee the mean-value exponential stability of an equilibrium solution associated with temporally uniform external inputs to the networks are obtained. One example is given to illustrate the theoretical results.

scholarly journals Stability Analysis for Stochastic Markovian Jump Reaction-Diffusion Neural Networks with Partially Known Transition Probabilities and Mixed Time Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Weiyuan Zhang ◽  
Junmin Li ◽  
Naizheng Shi
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Partial Information ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Reaction Diffusion ◽  
Stability Conditions ◽  
Markovian Jump ◽  
Mixed Time Delays ◽  
The Stability

The stability problem is proposed for a new class of stochastic Markovian jump reaction-diffusion neural networks with partial information on transition probability and mixed time delays. The new stability conditions are established in terms of linear matrix inequalities (LMIs). To reduce the conservatism of the stability conditions, an improved Lyapunov-Krasovskii functional and free-connection weighting matrices are introduced. The obtained results are dependent on delays and the measure of the space AND, therefore, have less conservativeness than delay-independent and space-independent ones. An example is given to show the effectiveness of the obtained results.

scholarly journals Exponential Synchronization for Stochastic Neural Networks with Mixed Time Delays and Markovian Jump Parameters via Sampled Data

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Yingwei Li ◽  
Xueqing Guo
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Exponential Synchronization ◽  
Stochastic Neural Networks ◽  
Sampled Data ◽  
Markovian Jump ◽  
Markovian Jump Parameters ◽  
Mixed Time Delays ◽  
Data Controller

The exponential synchronization issue for stochastic neural networks (SNNs) with mixed time delays and Markovian jump parameters using sampled-data controller is investigated. Based on a novel Lyapunov-Krasovskii functional, stochastic analysis theory, and linear matrix inequality (LMI) approach, we derived some novel sufficient conditions that guarantee that the master systems exponentially synchronize with the slave systems. The design method of the desired sampled-data controller is also proposed. To reflect the most dynamical behaviors of the system, both Markovian jump parameters and stochastic disturbance are considered, where stochastic disturbances are given in the form of a Brownian motion. The results obtained in this paper are a little conservative comparing the previous results in the literature. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals Robust Stabilization andH∞Control for Uncertain Neural Networks with Mixed Time Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Bin Wen ◽  
Hui Li ◽  
Li Liang
Keyword(s):  
Neural Networks ◽  
Robust Stability ◽  
Time Delays ◽  
Convex Combination ◽  
Robust Stabilization ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Mixed Time Delays ◽  
Uncertain Neural Networks

This paper is concerned with the problem of robust stabilization andH∞control for a class of uncertain neural networks. For the robust stabilization problem, sufficient conditions are derived based on the quadratic convex combination property together with Lyapunov stability theory. The feedback controller we design ensures the robust stability of uncertain neural networks with mixed time delays. We further design a robustH∞controller which guarantees the robust stability of the uncertain neural networks with a givenH∞performance level. The delay-dependent criteria are derived in terms of LMI (linear matrix inequality). Finally, numerical examples are provided to show the effectiveness of the obtained results.

scholarly journals Stability of Impulsive Cohen-Grossberg Neural Networks with Time-Varying Delays and Reaction-Diffusion Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jinhua Huang ◽  
Jiqing Liu ◽  
Guopeng Zhou
Keyword(s):  
Neural Networks ◽  
Boundary Condition ◽  
Diffusion Coefficients ◽  
Global Exponential Stability ◽  
Dirichlet Boundary ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Dirichlet Laplacian ◽  
The Stability

This work concerns the stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms as well as Dirichlet boundary condition. By means of Poincaré inequality and Gronwall-Bellman-type impulsive integral inequality, we summarize some new and concise sufficient conditions ensuring the global exponential stability of equilibrium point. The proposed criteria are relevant to the diffusion coefficients and the smallest positive eigenvalue of corresponding Dirichlet Laplacian. In conclusion, two examples are illustrated to demonstrate the effectiveness of our obtained results.

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