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

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.

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Existence and stability of periodic solution for mixed time-varying delayed neural networks with discontinuous activations

Neurocomputing ◽

10.1016/j.neucom.2013.06.038 ◽

2014 ◽

Vol 123 ◽

pp. 255-265 ◽

Cited By ~ 20

Author(s):

Lian Duan ◽

Lihong Huang ◽

Zuowei Cai

Keyword(s):

Neural Networks ◽

Periodic Solution ◽

Time Varying ◽

Delayed Neural Networks ◽

Discontinuous Activations ◽

Existence And Stability

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Fixed-time pinning-controlled synchronization for coupled delayed neural networks with discontinuous activations

Neural Networks ◽

10.1016/j.neunet.2019.04.010 ◽

2019 ◽

Vol 116 ◽

pp. 139-149 ◽

Cited By ~ 8

Author(s):

Hui Lü ◽

Wangli He ◽

Qing-Long Han ◽

Chen Peng

Keyword(s):

Neural Networks ◽

Fixed Time ◽

Delayed Neural Networks ◽

Discontinuous Activations

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Synchronization of Discontinuous Neural Networks with Delays via Adaptive Control

Discrete Dynamics in Nature and Society ◽

10.1155/2013/147164 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 6

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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