scholarly journals Robust fixed-time synchronization of discontinuous Cohen–Grossberg neural networks with mixed time delays

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Fanchao Kong ◽  
Quanxin Zhu ◽  
Feng Liang ◽  
Juan J. Nieto
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Time Synchronization ◽  
Distributed Delay ◽  
Fixed Time ◽  
Control Procedure ◽  
Mixed Time Delays ◽  
Analysis Theory ◽  
Response Systems ◽  
Functional Differential

This paper aims to investigate the fixed-time synchronization (i.e., synchronization in fixed-time sense) of Cohen–Grossberg drive-response neural networks with discontinuous neuron activations and mixed time delays (both time-varying discrete delay and distributed delay). To accomplish the target of fixed-time synchronization, a novel discontinuous feedback control procedure is firstly designed for the response neural networks. Then, under the framework of Filippov solutions, by means of functional differential inclusions theory, inequality technique and the nonsmooth analysis theory with Lyapunov-like approach, some sufficient criteria are derived to design the control parameters for achieving fixed-time synchronization of the proposed drive-response systems. Finally, two numerical examples are presented to illustrate the proposed methodologies.

Effects of mixed time delays and D operators on fixed-time synchronization of discontinuous neutral-type neural networks

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lin Sun ◽  
Fanchao Kong ◽  
Hongjun Qiu ◽  
Yanhong Zhang
Keyword(s):  
Neural Networks ◽  
Time Synchronization ◽  
Neutral Type ◽  
Fixed Time ◽  
Feedback Controllers ◽  
Control Laws ◽  
Mixed Time Delays ◽  
Inequality Technique ◽  
Error System ◽  
Functional Differential

Abstract In this paper, the fixed-time synchronization analysis is addressed for a class of discontinuous neutral-type neural networks. The focus is mainly on the design of useful control laws such that the constructed error system converges to zero in a fixed time. The major difficulty is to cope with the discontinuous neuron activations, D operators, time-varying discrete, and distributed delays simultaneously. To accomplish the target, a new and effective framework is firstly established. By means of functional differential inclusions theory, inequality technique and Lyapunov–Krasovskii functional, novel discontinuous feedback controllers are designed and some new verifiable algebraic criteria are derived to design the control gains. In contrast to the existed results on the neutral-type neural networks, the theoretical results of this paper are more general and rigorous. Finally, numerical examples and simulations are presented to illustrate the correctness of the main results.

ADAPTIVE SYNCHRONIZATION FOR UNKNOWN STOCHASTIC CHAOTIC NEURAL NETWORKS WITH MIXED TIME-DELAYS BY OUTPUT COUPLING

2008 ◽  
Vol 22 (24) ◽  
pp. 2391-2409 ◽  
Author(s):  
YANG TANG ◽  
JIAN-AN FANG ◽  
SUOJUN LU ◽  
QINGYING MIAO
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Distributed Delay ◽  
Adaptive Synchronization ◽  
Output Coupling ◽  
Stochastic Neural Networks ◽  
Unknown Parameters ◽  
Chaotic Neural Networks ◽  
Rigorous Approach ◽  
Mixed Time Delays

This paper is concerned with the synchronization problem for a class of stochastic neural networks with unknown parameters and mixed time-delays via output coupling. The mixed time-delays comprise the time-varying delay and distributed delay, and the neural networks are subjected to stochastic disturbances described in terms of a Brownian motion. Firstly, we use Lyapunov functions to establish general theoretical conditions for designing the output coupling matrix. Secondly, by using the adaptive feedback technique, a simple, analytical and rigorous approach is proposed to synchronize the stochastic neural networks with unknown parameters and mixed time-delays. Finally, numerical simulation results are given to show the effectiveness of the proposed method.

Fixed‐time synchronization for complex‐valued BAM neural networks with time delays

2019 ◽  
Author(s):  
Ziye Zhang ◽  
Runan Guo ◽  
Xiaoping Liu ◽  
Maiying Zhong ◽  
Chong Lin ◽  
...  
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Time Synchronization ◽  
Fixed Time ◽  
Bam Neural Networks ◽  
Complex Valued

Finite-time synchronization of coupled Cohen-Grossberg neural networks with mixed time delays

2020 ◽  
Vol 357 (16) ◽  
pp. 11349-11367
Author(s):  
Dongxue Peng ◽  
Jianxiang Li ◽  
Wei Xu ◽  
Xiaodi Li
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Time Delays ◽  
Time Synchronization ◽  
Mixed Time Delays

scholarly journals Dynamical Behaviors of the Stochastic Hopfield Neural Networks with Mixed Time Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Li Wan ◽  
Qinghua Zhou ◽  
Zhigang Zhou ◽  
Pei Wang
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Functional Differential Equations ◽  
Hopfield Neural Networks ◽  
Linear Matrix ◽  
Mixed Time Delays ◽  
Dynamical Behaviors ◽  
Functional Differential ◽  
Theoretical Results ◽  
Stochastic Functional

This paper investigates dynamical behaviors of the stochastic Hopfield neural networks with mixed time delays. The mixed time delays under consideration comprise both the discrete time-varying delays and the distributed time-delays. By employing the theory of stochastic functional differential equations and linear matrix inequality (LMI) approach, some novel criteria on asymptotic stability, ultimate boundedness, and weak attractor are derived. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

Finite-time synchronization for Cohen–Grossberg neural networks with mixed time-delays

2018 ◽  
Vol 294 ◽  
pp. 39-47 ◽  
Author(s):  
Dongxue Peng ◽  
Xiaodi Li ◽  
Chaouki Aouiti ◽  
Foued Miaadi
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Time Delays ◽  
Time Synchronization ◽  
Mixed Time Delays

scholarly journals Existence, Uniqueness, and Stability Analysis of Impulsive Neural Networks with Mixed Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Qiang Xi ◽  
Jianguo Si
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Sufficient Condition ◽  
Time Varying ◽  
Activation Functions ◽  
Mixed Time Delays

We study a class of impulsive neural networks with mixed time delays and generalized activation functions. The mixed delays include time-varying transmission delay, bounded time-varying distributed delay, and discrete constant delay in the leakage term. By using the contraction mapping theorem, we obtain a sufficient condition to guarantee the global existence and uniqueness of the solution for the addressed neural networks. In addition, a delay-independent sufficient condition for existence of an equilibrium point and some delay-dependent sufficient conditions for stability are derived, respectively, by using topological degree theory and Lyapunov-Krasovskii functional method. The presented results require neither the boundedness, monotonicity, and differentiability of the activation functions nor the differentiability (even differential boundedness) of time-varying delays. Moreover, the proposed stability criteria are given in terms of linear matrix inequalities (LMI), which can be conveniently checked by the MATLAB toolbox. Finally, an example is given to show the effectiveness and less conservativeness of the obtained results.

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