scholarly journals Synchronization for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms

2016 ◽  
Vol 21 (3) ◽  
pp. 379-399 ◽  
Author(s):  
Qintao Gan ◽  
Tielin Liu ◽  
Chang Liu ◽  
Tianshi Lv
Keyword(s):  
Neural Networks ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Dirichlet Boundary Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Interval Time ◽  
Generalized Neural Networks ◽  
Special Cases

In this paper, the synchronization problem for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms is investigated under Dirichlet boundary conditions and Neumann boundary conditions, respectively. Based on Lyapunov stability theory, both delay-derivative-dependent and delay-range-dependent conditions are derived in terms of linear matrix inequalities (LMIs), whose solvability heavily depends on the information of reaction-diffusion terms. The proposed generalized neural networks model includes reaction-diffusion local field neural networks and reaction-diffusion static neural networks as its special cases. The obtained synchronization results are easy to check and improve upon the existing ones. In our results, the assumptions for the differentiability and monotonicity on the activation functions are removed. It is assumed that the state delay belongs to a given interval, which means that the lower bound of delay is not restricted to be zero. Finally, the feasibility and effectiveness of the proposed methods is shown by simulation examples.

GLOBAL EXPONENTIAL STABILITY OF REACTION-DIFFUSION TIME-VARYING DELAYED CELLULAR NEURAL NETWORKS WITH DIRICHLET BOUNDARY CONDITIONS

2009 ◽  
Vol 02 (03) ◽  
pp. 377-389
Author(s):  
JIANGHONG BAI ◽  
ZHIDONG TENG ◽  
HAIJUN JIANG
Keyword(s):  
Neural Networks ◽  
Boundary Conditions ◽  
Exponential Stability ◽  
Global Exponential Stability ◽  
Dirichlet Boundary ◽  
Reaction Diffusion ◽  
Cellular Neural Networks ◽  
Diffusion Time ◽  
Dirichlet Boundary Conditions ◽  
Time Varying

This paper is devoted to global exponential stability of reaction-diffusion time-varying delayed cellular neural networks with Dirichlet boundary conditions. Without assuming the monotonicity and differentiability of activation functions, nor symmetry of synaptic interconnection weights, the authors present some delay independent and easily verifiable sufficient conditions to ensure the global exponential stability of the equilibrium solution by using the method of variational parameter and inequality technique. These conditions obtained have important leading significance in the designs and applications of global exponential stability for reaction-diffusion neural circuit systems with delays. Lastly, one example is given to illustrate the theoretical analysis.

scholarly journals Passivity Analysis of Markov Jumping Delayed Reaction-Diffusion Neural Networks under Different Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Ziwei Li ◽  
Xuelian Wang ◽  
Qingkai Kong ◽  
Jing Wang
Keyword(s):  
Neural Networks ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
Delayed Reaction ◽  
Integral Term ◽  
Inequality Techniques ◽  
Delay Dependent ◽  
Delay Dependent Stability

This work analyzes the passivity for a set of Markov jumping reaction-diffusion neural networks limited by time-varying delays under Dirichlet and Neumann boundary conditions, respectively, in which Markov jumping is used to describe the variations among system parameters. To overcome some difficulties originated from partial differential terms, the Lyapunov–Krasovskii functional that introduces a new integral term is proposed and some inequality techniques are also adopted to obtain the delay-dependent stability conditions in terms of linear matrix inequalities, which ensures that the designed neural networks satisfy the specified performance of passivity. Finally, the advantages and effectiveness of the obtained results are verified via displaying two illustrated examples.

scholarly journals Robust Synchronization Criterion for Coupled Stochastic Discrete-Time Neural Networks with Interval Time-Varying Delays, Leakage Delay, and Parameter Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Leakage Term ◽  
Interval Time ◽  
Robust Synchronization ◽  
Delay Dependent ◽  
Finsler’S Lemma

The purpose of this paper is to investigate a delay-dependent robust synchronization analysis for coupled stochastic discrete-time neural networks with interval time-varying delays in networks coupling, a time delay in leakage term, and parameter uncertainties. Based on the Lyapunov method, a new delay-dependent criterion for the synchronization of the networks is derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii’s functional and utilizing Finsler’s lemma without free-weighting matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

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.

Stability of Markovian Jump Generalized Neural Networks With Interval Time-Varying Delays

2017 ◽  
Vol 28 (8) ◽  
pp. 1840-1850 ◽  
Author(s):  
Ramasamy Saravanakumar ◽  
Muhammed Syed Ali ◽  
Choon Ki Ahn ◽  
Hamid Reza Karimi ◽  
Peng Shi
Keyword(s):  
Neural Networks ◽  
Time Varying ◽  
Markovian Jump ◽  
Interval Time ◽  
Generalized Neural Networks

Asymptotic behaviour of some reaction-diffusion systems modelling complex combustion on bounded domains

1993 ◽  
Vol 123 (6) ◽  
pp. 1151-1163
Author(s):  
Joel D. Avrin
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Convergence Result ◽  
Decay Rates ◽  
Dirichlet Boundary Conditions ◽  
Reaction Diffusion Systems ◽  
Convergence Results ◽  
Mass Fractions

SynopsisWe consider three models of multiple-step combustion processes on bounded spatial domains. Previously, steady-state convergence results have been established for these models with zero Neumann boundary conditions imposed on the temperature as well as the mass fractions. We retain here throughout the same boundary conditions on the mass fractions, but in our first set of results we establish steady-state convergence results with fixed Dirichlet boundary conditions on the temperature. Next, under certain physically reasonable assumptions, we develop, for two of the models, estimates on the decay rates of both mass fractions to zero, while for the remaining model we develop estimates on the decay rate of one concentration to zero and establish a positive lower bound on the other mass fraction. These results hold under either set of boundary conditions, but when the Dirichlet conditions are imposed on the temperature, we are able to obtain estimates on the rate of convergence of the temperature to its (generally nonconstant) steady-state. Finally, we improve the results of a previous paper by adding a temperature convergence result.

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