Periodicity and global exponential periodic synchronization of delayed neural networks with discontinuous activations and impulsive perturbations

2021 ◽  
Vol 431 ◽  
pp. 111-127
Author(s):  
Zhilong He ◽  
Chuandong Li ◽  
Zhengran Cao ◽  
Hongfei Li
Keyword(s):  
Neural Networks ◽  
Delayed Neural Networks ◽  
Discontinuous Activations ◽  
Impulsive Perturbations

Finite‐Time Synchronization of Complex‐Valued Delayed Neural Networks with Discontinuous Activations

2018 ◽  
Vol 20 (6) ◽  
pp. 2237-2247 ◽  
Author(s):  
Enli Wu ◽  
Xinsong Yang ◽  
Chen Xu ◽  
Fuad E. Alsaadi ◽  
Tasawar Hayat
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Time Synchronization ◽  
Delayed Neural Networks ◽  
Discontinuous Activations ◽  
Complex Valued

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.

scholarly journals Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xinsong Yang ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Adaptive Control ◽  
Control Technique ◽  
Activation Functions ◽  
Complete Synchronization ◽  
Delayed Neural Networks ◽  
Discontinuous Activation ◽  
Discontinuous Activations ◽  
Discontinuous Activation Functions ◽  
Continuous Neural Networks

The drive-response synchronization of delayed neural networks with discontinuous activation functions is investigated via adaptive control. The synchronization of this paper means that the synchronization error approaches to zero for almost all time as time goes to infinity. The discontinuous activation functions are assumed to be monotone increasing which can be unbounded. Due to the mild condition on the discontinuous activations, adaptive control technique is utilized to control the response system. Under the framework of Filippov solution, by using Lyapunov function and chain rule of differential inclusion, rigorous proofs are given to show that adaptive control can realize complete synchronization of the considered model. The results of this paper are also applicable to continuous neural networks, since continuous function is a special case of discontinuous function. Numerical simulations verify the effectiveness of the theoretical results. Moreover, when there are parameter mismatches between drive and response neural networks with discontinuous activations, numerical example is also presented to demonstrate the complete synchronization by using discontinuous adaptive control.

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