scholarly journals Synchronization of Switched Interval Networks and Applications to Chaotic Neural Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jinde Cao ◽  
Abdulaziz Alofi ◽  
Abdullah Al-Mazrooei ◽  
Ahmed Elaiw
Keyword(s):  
Neural Networks ◽  
Matrix Measure ◽  
Chaotic Neural Networks ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Arbitrary Switching ◽  
Parameters Uncertainty ◽  
Inequality Technique ◽  
Error System ◽  
Switched Interval Networks

This paper investigates synchronization problem of switched delay networks with interval parameters uncertainty, based on the theories of the switched systems and drive-response technique, a mathematical model of the switched interval drive-response error system is established. Without constructing Lyapunov-Krasovskii functions, introducing matrix measure method for the first time to switched time-varying delay networks, combining Halanay inequality technique, synchronization criteria are derived for switched interval networks under the arbitrary switching rule, which are easy to verify in practice. Moreover, as an application, the proposed scheme is then applied to chaotic neural networks. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results.

scholarly journals Adaptive Synchronization for a Class of Cellular Neural Networks with Pantograph Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Xuehui Mei ◽  
Jiuju Xing ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Liwei Zhang
Keyword(s):  
Neural Networks ◽  
Lyapunov Functional ◽  
Cellular Neural Networks ◽  
Feedback Controller ◽  
Adaptive Synchronization ◽  
Functional Theory ◽  
Adaptive Feedback ◽  
Synchronization Problem ◽  
Inequality Technique

This paper deals with the synchronization problem for a class of cellular neural networks with pantograph delays. By using Lyapunov functional theory and inequality technique, some new and useful results are obtained for asymptotical synchronization under adaptive feedback controller.

Improved Results on Adaptive Control Approach for Projective Synchronization of Neural Networks with Time-Varying Delay

2019 ◽  
Vol 20 (6) ◽  
pp. 623-631 ◽  
Author(s):  
Abdujelil Abdurahman ◽  
Malika Sader ◽  
Haijun Jiang
Keyword(s):  
Neural Networks ◽  
Functional Method ◽  
Mean Value ◽  
Projective Synchronization ◽  
Mean Value Theorem ◽  
Time Varying ◽  
Chaotic Neural Networks ◽  
Control Approach ◽  
Time Varying Delay ◽  
Varying Delay

AbstractCompared to other types of synchronization such as complete synchronization and lag synchronization, there is a unique advantage in projective synchronization since it can greatly improve the security of communication. In this paper, the projective synchronization problem of a class of chaotic neural networks with time-varying delay is investigated via designing a novel adaptive controller. Some simple and useful criteria are derived by employing Lyapunov functional method and Lagrange mean value theorem. Finally, an example and its numerical simulations are given to demonstrate the effectiveness of the proposed control schemes. It is worth to mention that the designed controller in this paper dos not require any knowledge about the activation functions, which can be seen the main novelty of the paper.

Stochastic synchronization of neutral-type chaotic impulse neural networks with leakage delay and Markovian jumping parameters

2016 ◽  
Vol 9 (3) ◽  
pp. 237-254 ◽  
Author(s):  
Cheng-De Zheng ◽  
Zhanshan Wang
Keyword(s):  
Neural Networks ◽  
Neutral Type ◽  
Leakage Delay ◽  
Markovian Jumping Parameters ◽  
Activation Functions ◽  
Markovian Jumping ◽  
Content Type ◽  
Chaotic Neural Networks ◽  
Synchronization Problem ◽  
Impulsive Perturbations

Purpose The purpose of this paper is to develop a methodology for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations. Design/methodology/approach The authors perform drive-response concept and time-delay feedback control techniques to investigate a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations. New sufficient criterion is established without strict conditions imposed on the activation functions. Findings It turns out that the approach results in new sufficient criterion easy to be verified but without the usual assumption of the differentiability and monotonicity of the activation functions. Two examples show the effectiveness of the obtained results. Originality/value The novelty of the proposed approach lies in removing the usual assumption of the differentiability and monotonicity of the activation functions, and the use of the Lyapunov functional method, Jensen integral inequality, a novel Gu’s lemma, reciprocal convex and linear convex combination technique for the stochastically asymptotic synchronization problem for a class of neutral-type chaotic neural networks with both leakage delay and Markovian jumping parameters under impulsive perturbations.

scholarly journals Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 101 ◽  
Author(s):  
Jinlong Shu ◽  
Lianglin Xiong ◽  
Tao Wu ◽  
Zixin Liu
Keyword(s):  
Neural Networks ◽  
Convex Combination ◽  
Neutral Type ◽  
Stability Conditions ◽  
Time Varying ◽  
Time Varying Delay ◽  
Convex Inequality ◽  
Inequality Technique ◽  
Combination Approach ◽  
Complex Valued

This paper addresses the problem of global μ -stability for quaternion-valued neutral-type neural networks (QVNTNNs) with time-varying delays. First, QVNTNNs are transformed into two complex-valued systems by using a transformation to reduce the complexity of the computation generated by the non-commutativity of quaternion multiplication. A new convex inequality in a complex field is introduced. In what follows, the condition for the existence and uniqueness of the equilibrium point is primarily obtained by the homeomorphism theory. Next, the global stability conditions of the complex-valued systems are provided by constructing a novel Lyapunov–Krasovskii functional, using an integral inequality technique, and reciprocal convex combination approach. The gained global μ -stability conditions can be divided into three different kinds of stability forms by varying the positive continuous function μ ( t ) . Finally, three reliable examples and a simulation are given to display the effectiveness of the proposed methods.

scholarly journals Finite-Time Synchronizing Control for Chaotic Neural Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Chao Zhang ◽  
Qiang Guo ◽  
Jing Wang
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Control Method ◽  
High Gain ◽  
Singular Perturbation Theory ◽  
External Disturbances ◽  
Chaotic Neural Networks ◽  
Finite Time Stability ◽  
Master System ◽  
Error System

This paper addresses the finite-time synchronizing problem for a class of chaotic neural networks. In a real communication network, parameters of the master system may be time-varying and the system may be perturbed by external disturbances. A simple high-gain observer is designed to track all the nonlinearities, unknown system functions, and disturbances. Then, a dynamic active compensatory controller is proposed and by using the singular perturbation theory, the control method can guarantee the finite-time stability of the error system between the master system and the slave system. Finally, two illustrative examples are provided to show the effectiveness and applicability of the proposed scheme.

ROBUST SYNCHRONIZATION CRITERIA FOR RECURRENT NEURAL NETWORKS VIA LINEAR FEEDBACK

2007 ◽  
Vol 17 (08) ◽  
pp. 2723-2738 ◽  
Author(s):  
XIA HUANG ◽  
JAMES LAM ◽  
JINDE CAO ◽  
SHENGYUAN XU
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Linear Feedback ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Synchronization Problem ◽  
Robust Synchronization ◽  
Control Robustness ◽  
Delay Dependent

In this paper, the robust synchronization problem is addressed for recurrent neural networks with time-varying delay by linear feedback control. Robustness in the present paper is referred to as the allowance of parameters mismatch between the drive system and the response system. Sufficient conditions for robust synchronization with a synchronization error bound, expressed as linear matrix inequality (LMI), are derived based on Lyapunov–Krasovskii functionals. Both delay-dependent and delay-independent conditions are obtained. Two examples are given to illustrate the results.

scholarly journals Finite-/fixed-time synchronization of delayed Clifford-valued recurrent neural networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
N. Boonsatit ◽  
G. Rajchakit ◽  
R. Sriraman ◽  
C. P. Lim ◽  
P. Agarwal
Keyword(s):  
Neural Networks ◽  
Recurrent Neural Networks ◽  
Time Synchronization ◽  
Fixed Time ◽  
Computational Techniques ◽  
Feedback Controllers ◽  
System Models ◽  
Response System ◽  
Synchronization Problem ◽  
Error System

AbstractThis paper investigates the problem of finite-/fixed-time synchronization for Clifford-valued recurrent neural networks with time-varying delays. The considered Clifford-valued drive and response system models are firstly decomposed into real-valued drive and response system models in order to overcome the difficulty of the noncommutativity of the multiplication of Clifford numbers. Then, suitable time-delayed feedback controllers are devised to investigate the synchronization problem in finite-/fixed-time of error system. On the basis of new Lyapunov–Krasovskii functional and new computational techniques, finite-/fixed-time synchronization criteria are formulated for the corresponding real-valued drive and response system models. Two numerical examples demonstrate the effectiveness of the theoretical results.

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