GENERALIZED PROJECTIVE SYNCHRONIZATION OF A CLASS OF DELAYED NEURAL NETWORKS

2008 ◽  
Vol 22 (03) ◽  
pp. 181-190 ◽  
Author(s):  
JUAN MENG ◽  
XINGYUAN WANG
Keyword(s):  
Neural Networks ◽  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theorem ◽  
Projective Synchronization ◽  
Lyapunov Stability Theorem ◽  
Delayed Neural Networks ◽  
Generalized Projective Synchronization

In this paper, the generalized projective synchronization of a class of delayed neural networks is investigated. Based on the Lyapunov stability theorem, a kind of controller is designed. The generalized projective synchronization of delayed neural networks can be achieved by using this kind of controller. Theoretical analysis and numerical simulations are provided to verify the feasibility and effectiveness of the proposed scheme.

scholarly journals Synchronization of Chaotic Delayed Neural Networks via Impulsive Control

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Yang Fang ◽  
Kang Yan ◽  
Kelin Li
Keyword(s):  
Neural Networks ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Lyapunov Stability Theorem ◽  
Delayed Neural Networks ◽  
Impulsive Synchronization ◽  
Synchronization Problem

This paper is concerned with the impulsive synchronization problem of chaotic delayed neural networks. By employing Lyapunov stability theorem, impulsive control theory and linear matrix inequality (LMI) technique, several new sufficient conditions ensuring the asymptotically synchronization for coupled chaotic delayed neural networks are derived. Based on these new sufficient conditions, an impulsive controller is designed. Moreover, the stable impulsive interval of synchronized neural networks is objectively estimated by combining the MATLAB LMI toolbox and one of the two given equations. Two examples with numerical simulations are given to illustrate the effectiveness of the proposed method.

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

GENERALIZED PROJECTIVE SYNCHRONIZATION OF CHAOTIC NEURAL NETWORKS: OBSERVER-BASED APPROACH

2010 ◽  
Vol 24 (17) ◽  
pp. 3351-3363 ◽  
Author(s):  
XING YUAN WANG ◽  
JUAN MENG
Keyword(s):  
Neural Networks ◽  
Numerical Simulations ◽  
State Observer ◽  
Projective Synchronization ◽  
Pole Placement ◽  
Chaotic Neural Networks ◽  
Generalized Projective Synchronization ◽  
Synchronization Scheme ◽  
Placement Technique ◽  
Nonlinear State

In this paper, the generalized projective synchronization of chaotic neural networks is investigated. Based on the modified nonlinear state observer algorithm and the pole placement technique, a synchronization scheme is designed. The generalized projective synchronization of different chaotic neural networks can be achieved by using the proposed method. Numerical simulations further demonstrate the effectiveness of the proposed scheme.

Application of Synchronization Control Method to Zagzag System

2012 ◽  
Vol 241-244 ◽  
pp. 1067-1070
Author(s):  
Yin Li ◽  
Chun Long Zheng
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Control Method ◽  
Stability Theorem ◽  
Synchronization Control ◽  
Lyapunov Stability Theorem ◽  
Synchronization Scheme

In this paper, synchronization control method of Zagzag system is discussed both theoretically and numerically. Based on the Lyapunov stability theorem and the chaotic methods, synchronization control is given and illustrated with Zagzag system as example. Numerical simulations are presented to demonstrate the effectiveness of the proposed synchronization scheme.

GENERALIZED PROJECTIVE SYNCHRONIZATION AND PARAMETERS ESTIMATION OF TWO NEW HYPERCHAOTIC SYSTEMS WITH FULLY UNCERTAIN PARAMETERS

2010 ◽  
Vol 21 (02) ◽  
pp. 249-259 ◽  
Author(s):  
CONG-XU ZHU
Keyword(s):  
Adaptive Control ◽  
Adaptive Controller ◽  
Stability Theorem ◽  
Parameters Estimation ◽  
Projective Synchronization ◽  
Uncertain Parameters ◽  
Lyapunov Stability Theorem ◽  
Generalized Projective Synchronization ◽  
Hyperchaotic Systems ◽  
Theoretical Results

This paper investigates adaptive generalized projective synchronization (GPS) between two novel hyperchaotic systems with different structure and fully uncertain parameters. Based on the Lyapunov stability theorem and the adaptive control theory, GPS between the two hyperchaotic systems is achieved by proposing a new adaptive controller and a novel parameters estimation update law. Strict theoretical proof is put forward. Numerical simulations are presented to demonstrate the effectiveness of the proposed GPS scheme and verify the theoretical results.

scholarly journals Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaobing Zhou ◽  
Lianglin Xiong ◽  
Xiaomei Cai
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Chaotic Systems ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Combination Synchronization ◽  
Special Cases ◽  
Complex Chaotic Systems

This paper investigates the combination-combination synchronization of four nonlinear complex chaotic systems. Based on the Lyapunov stability theory, corresponding controllers to achieve combination-combination synchronization among four different nonlinear complex chaotic systems are derived. The special cases, such as combination synchronization and projective synchronization, are studied as well. Numerical simulations are given to illustrate the theoretical analysis.

scholarly journals Synchronization and Lag Synchronization of Hyperchaotic Memristor-Based Chua’s Circuits

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Junjian Huang ◽  
Chuandong Li ◽  
Tingwen Huang ◽  
Hui Wang ◽  
Xin Wang
Keyword(s):  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theorem ◽  
Chua’S Circuit ◽  
Lyapunov Stability Theorem ◽  
Lag Synchronization ◽  
Chua's Circuit ◽  
Initial Values ◽  
Theoretical Results

A memristor-based five-dimensional (5D) hyperchaotic Chua’s circuit is proposed. Based on the Lyapunov stability theorem, the controllers are designed to realize the synchronization and lag synchronization between the hyperchaotic memristor-based Chua’s circuits under different initial values, respectively. Numerical simulations are also presented to show the effectiveness and feasibility of the theoretical results.

scholarly journals Generalized Projective Synchronization for Different Hyperchaotic Dynamical Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. M. El-Dessoky ◽  
E. Saleh
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Lorenz System ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Hyperchaotic Lorenz System ◽  
Generalized Projective Synchronization ◽  
Hyperchaotic Systems

Projective synchronization and generalized projective synchronization have recently been observed in the coupled hyperchaotic systems. In this paper a generalized projective synchronization technique is applied in the hyperchaotic Lorenz system and the hyperchaotic Lü. The sufficient conditions for achieving projective synchronization of two different hyperchaotic systems are derived. Numerical simulations are used to verify the effectiveness of the proposed synchronization techniques.

Improved Control Schemes for Projective Synchronization of Delayed Neural Networks with Unmatched Coefficients

2019 ◽  
Vol 34 (03) ◽  
pp. 2051005 ◽  
Author(s):  
Abdujelil Abdurahman ◽  
Haijun Jiang
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Chaos Synchronization ◽  
Projective Synchronization ◽  
Chaotic Neural Networks ◽  
Delayed Neural Networks ◽  
Mixed Time Delays ◽  
Control Schemes ◽  
Master System ◽  
Inequality Techniques

Projective synchronization (PS) is a type of chaos synchronization where the states of slave system are scaled replicas of the states of master system. This paper studies the asymptotic projective synchronization (APS) between master–slave chaotic neural networks (NNs) with mixed time-delays and unmatched coefficients. Based on useful inequality techniques and constructing a suitable Lyapunov functional, some simple criteria are derived to ensure the APS of considered networks via designing a novel adaptive feedback controller. In addition, a numerical example and its MATLAB simulations are provided to check the feasibility of the obtained results. The main innovation of our work is that we dealt with the APS problem between two different chaotic NNs, while most of the existing works only concerned with the PS of chaotic systems with the same topologies. In addition, compared with the controllers introduced in the existing papers, the designed controller in this paper does not require any knowledge about the activation functions, which can be seen as another novelty of the paper.

CONSTRUCTIVE APPROACHES FOR TRAINING OF WAVELET NEURAL NETWORKS USING ADAPTIVE LEARNING RATE

2013 ◽  
Vol 11 (03) ◽  
pp. 1350021
Author(s):  
MOHAMED ZINE EL ABIDINE SKHIRI ◽  
MOHAMED CHTOUROU
Keyword(s):  
Neural Networks ◽  
Adaptive Learning ◽  
Fixed Number ◽  
Stability Theorem ◽  
Learning Rate ◽  
Training Algorithms ◽  
Lyapunov Stability Theorem ◽  
Constructive Approach ◽  
Wavelet Neural Networks ◽  
Adaptive Learning Rate

This paper investigates the applicability of the constructive approach proposed in Ref. 1 to wavelet neural networks (WNN). In fact, two incremental training algorithms will be presented. The first one, known as one pattern at a time (OPAT) approach, is the WNN version of the method applied in Ref. 1. The second approach however proposes a modified version of Ref. 1, known as one epoch at a time (OEAT) approach. In the OPAT approach, the input patterns are trained incrementally one by one until all patterns are presented. If the algorithm gets stuck in a local minimum and could not escape after a fixed number of successive attempts, then a new wavelet called also wavelon, will be recruited. In the OEAT approach however, all the input patterns are presented one epoch at a time. During one epoch, each pattern is trained only once until all patterns are trained. If the resulting overall error is reduced, then all the patterns will be retrained for one more epoch. Otherwise, a new wavelon will be recruited. To guarantee the convergence of the trained networks, an adaptive learning rate has been introduced using the discrete Lyapunov stability theorem.

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