GLOBAL SYNCHRONIZATION IN AN ARRAY OF LINEARLY COUPLED DELAYED NEURAL NETWORKS WITH AN ARBITRARY COUPLING MATRIX

2006 ◽  
Vol 16 (11) ◽  
pp. 3357-3368 ◽  
Author(s):  
HONGTAO LU ◽  
GUANRONG CHEN
Keyword(s):  
Neural Networks ◽  
Numerical Simulations ◽  
Output Coupling ◽  
Sufficient Condition ◽  
Global Synchronization ◽  
Coupling Matrix ◽  
Delayed Neural Networks ◽  
Arbitrary Coupling ◽  
General Sufficient Condition ◽  
Theoretical Results

In this paper, we investigate global synchronization in an array of linearly coupled identical delayed neural networks. We consider the array with an arbitrary coupling matrix without assuming it to be symmetric, irreducible and diffusive. Moreover, we consider the array being connected through two different coupling schemes, state-coupling and output-coupling, respectively. For state-coupling, we derive a more general sufficient condition ensuring global synchronization, which is an extension of some existing results in the literature. For output-coupling, we derive a new sufficient condition for global synchronization. Numerical simulations are given to illustrate the theoretical results.

GLOBAL SYNCHRONIZATION OF COUPLED DELAYED NEURAL NETWORKS AND APPLICATIONS TO CHAOTIC CNN MODELS

2004 ◽  
Vol 14 (07) ◽  
pp. 2229-2240 ◽  
Author(s):  
GUANRONG CHEN ◽  
JIN ZHOU ◽  
ZENGRONG LIU
Keyword(s):  
Neural Networks ◽  
Lyapunov Functional ◽  
Matrix Theory ◽  
Hermitian Matrix ◽  
Sufficient Condition ◽  
Global Synchronization ◽  
Coupling Matrix ◽  
Chaotic Neural Networks ◽  
Delayed Neural Networks ◽  
Functional Methods

This paper formulates the model and then studies its dynamics of a system of linearly and diffusively coupled identical delayed neural networks (DNNs), which is generalization of delayed Hopfied neural networks (DHNNs) and delayed cellular neural networks (DCNNs). In particularly, a simple yet generic sufficient condition for global synchronization of such coupled DNNs is derived based on the Lyapunov functional methods and Hermitian matrix theory. It is shown that global synchronization of coupled DNNs is ensured by a suitable design of the coupling matrix and the inner linking matrix. Furthermore, the result is applied to some typical chaotic neural networks. Finally, numerical simulations are presented to demonstrate the effectiveness of the approach.

scholarly journals Achieving Synchronization in Arrays of Coupled Differential Systems with Time-Varying Couplings

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Xinlei Yi ◽  
Wenlian Lu ◽  
Tianping Chen
Keyword(s):  
Reaction Dynamics ◽  
Largest Lyapunov Exponent ◽  
Sufficient Condition ◽  
Time Varying ◽  
Complete Synchronization ◽  
Coupling Matrix ◽  
Differential Systems ◽  
General Sufficient Condition ◽  
Theoretical Results ◽  
Ordinary Differential Equation Systems

We study complete synchronization of the complex dynamical networks described by linearly coupled ordinary differential equation systems (LCODEs). Here, the coupling is timevarying in both network structure and reaction dynamics. Inspired by our previous paper (Lu et al. (2007-2008)), the extended Hajnal diameter is introduced and used to measure the synchronization in a general differential system. Then we find that the Hajnal diameter of the linear system induced by the time-varying coupling matrix and the largest Lyapunov exponent of the synchronized system play the key roles in synchronization analysis of LCODEs with identity inner coupling matrix. As an application, we obtain a general sufficient condition guaranteeing directed time-varying graph to reach consensus. Example with numerical simulation is provided to show the effectiveness of the theoretical results.

scholarly journals New Methods of Finite-Time Synchronization for a Class of Fractional-Order Delayed Neural Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Weiwei Zhang ◽  
Jinde Cao ◽  
Ahmed Alsaedi ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Finite Time Interval ◽  
Delayed Neural Networks ◽  
New Methods ◽  
Theoretical Results

Finite-time synchronization for a class of fractional-order delayed neural networks with fractional order α, 0<α≤1/2 and 1/2<α<1, is investigated in this paper. Through the use of Hölder inequality, generalized Bernoulli inequality, and inequality skills, two sufficient conditions are considered to ensure synchronization of fractional-order delayed neural networks in a finite-time interval. Numerical example is given to verify the feasibility of the theoretical results.

scholarly journals Global Synchronization in Complex Networks with Adaptive Coupling

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Zhengzhong Yuan ◽  
Jianping Cai ◽  
Meili Lin
Keyword(s):  
Complex Networks ◽  
Numerical Simulations ◽  
Adaptive Controller ◽  
Asymptotically Stable ◽  
State Variables ◽  
Global Synchronization ◽  
Coupling Matrix ◽  
Unified Chaotic System ◽  
Adaptive Coupling ◽  
Partial State

Global synchronization in adaptive coupling networks is studied in this paper. A new simple adaptive controller is proposed based on a concept of asymptotically stable led by partial state variables. Under the proposed adaptive update law, the network can achieve global synchronization without calculating the eigenvalues of the outer coupling matrix. The update law is only dependent on partial state variables of individual oscillators. Numerical simulations are given to show the effectiveness of the proposed method, in which the unified chaotic system is chosen as the nodes of the network with different topologies.

scholarly journals Combined Convex Technique on Delay-Distribution-Dependent Stability for Delayed Neural Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Ting Wang ◽  
Tao Li ◽  
Mingxiang Xue ◽  
Shumin Fei
Keyword(s):  
Neural Networks ◽  
Functional Approach ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Mean Square ◽  
Variable Delay ◽  
Delayed Neural Networks ◽  
The Mean ◽  
Delay Partitioning ◽  
Delay Variation

Together with the Lyapunov-Krasovskii functional approach and an improved delay-partitioning idea, one novel sufficient condition is derived to guarantee a class of delayed neural networks to be asymptotically stable in the mean-square sense, in which the probabilistic variable delay and both of delay variation limits can be measured. Through combining the reciprocal convex technique and convex technique one, the criterion is presented via LMIs and its solvability heavily depends on the sizes of both time-delay range and its variations, which can become much less conservative than those present ones by thinning the delay intervals. Finally, it can be demonstrated by four numerical examples that our idea reduces the conservatism more effectively than some earlier reported ones.

AN EFFICIENT MULTI-SPIN CODING ALGORITHM FOR NEURAL NETWORKS

1991 ◽  
Vol 02 (02) ◽  
pp. 623-636 ◽  
Author(s):  
MARTIN NESCHEN
Keyword(s):  
Neural Networks ◽  
Numerical Simulations ◽  
High Speed ◽  
Large Scale ◽  
Effective Rate ◽  
Computational Effort ◽  
Local Fields ◽  
New Method ◽  
Coupling Matrix ◽  
Horizontal Structure

A new method for large-scale numerical simulations of neural networks is proposed which reduces the computational effort by incrementally updating the local fields and thus restricting the operations to flipped spins only. A highly optimized multi-spin algorithm is described employing words oriented along the columns of the coupling matrix unlike the horizontal structure in existing high-speed algorithms. An effective rate of 35*109 couplings/s on a Cray-YMP can be attained which is about five times as fast as best existing multi-spin implementations.

General Decay Synchronization for Fuzzy Cellular Neural Networks with Time-Varying Delays

2019 ◽  
Vol 20 (5) ◽  
pp. 551-560 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Abdujelil Abdurahman
Keyword(s):  
Neural Networks ◽  
Numerical Simulations ◽  
Cellular Neural Networks ◽  
General Decay ◽  
Time Varying ◽  
Fuzzy Cellular Neural Networks ◽  
Activation Functions ◽  
General Activation ◽  
Inequality Techniques ◽  
Theoretical Results

AbstractThis paper studies the general decay synchronization (GDS) of a class of fuzzy cellular neural networks (FCNNs) with general activation functions and time-varying delays. By introducing suitable Lyapunov-Krasovskii functionals and employing useful inequality techniques, some novel criteria ensuring the GDS of considered FCNNs are established via a type of nonlinear control. In addition, two examples with numerical simulations are presented to illustrate the obtained theoretical results.

Dynamics of a stochastic rabies epidemic model with markovian switching

2021 ◽  
pp. 2150032
Author(s):  
Hao Peng ◽  
Xinhong Zhang ◽  
Daqing Jiang
Keyword(s):  
Lyapunov Function ◽  
White Noise ◽  
Numerical Simulations ◽  
Positive Solution ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Telegraph Noise ◽  
Global Positive Solution ◽  
Theoretical Results

In this paper, we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise. First, we prove the existence of the unique global positive solution. Second, by constructing an appropriate Lyapunov function, we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for the extinction of diseases. Finally, numerical simulations are introduced to illustrate our theoretical results.

COMPLETE PERIODIC SYNCHRONIZATION OF DELAYED NEURAL NETWORKS WITH DISCONTINUOUS ACTIVATIONS

2010 ◽  
Vol 20 (07) ◽  
pp. 2151-2164 ◽  
Author(s):  
XIAOYANG LIU ◽  
JINDE CAO ◽  
GAN HUANG
Keyword(s):  
Neural Networks ◽  
Control Method ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Discontinuous Activations ◽  
Potential Applications ◽  
Error System ◽  
Discontinuous Activation Functions ◽  
Necessary And Sufficient ◽  
Theoretical Results

Recently, the synchronization issue in chaotic systems has become a hot topic in nonlinear dynamics and has aroused great interest among researchers due to the theoretical significance and potential applications. In this paper, complete periodic synchronization is considered for the delayed neural networks with discontinuous activation functions. Under the framework of Filippov solution, a novel control method is presented by using differential inclusions theory, nonsmooth Lyapunov method and linear matrix inequality (LMI) approach. Based on a newly obtained necessary and sufficient condition, several criteria are derived to ensure the global asymptotical stability of the error system, and thus the response system synchronizes with the drive system. Moreover, the estimation gains are obtained. With these new and effective methods, complete synchronization is achieved. Simulation results are given to illustrate the theoretical results.

Synchronization and Anti-Synchronization of the Chaotic Modified Chua's Circuits via a Same Controller

2012 ◽  
Vol 605-607 ◽  
pp. 1972-1975
Author(s):  
Jian Cai Leng ◽  
Rong Wei Guo
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Global Synchronization ◽  
Single Input ◽  
Theoretical Results

Based on the Lyapunov stability theorem, a same controller in the form is designed to achieve the global synchronization and anti-synchronization of the chaotic modified Chua's circuits. The controller obtained in this paper is simpler than those obtained in the existing results, and it is a linear single input controller. Numerical simulations verify the correctness and the effectiveness of the proposed theoretical results

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