General decay anti-synchronization of multi-weighted coupled neural networks with and without reaction–diffusion terms

  • Yanli HuangEmail author
  • Jie Hou
  • Erfu Yang
Original Article


The network models of multi-weighted coupled neural networks (MWCNNs) and multi-weighted coupled reaction–diffusion neural networks (MWCRDNNs) with and without delayed coupling are presented in this paper, respectively. Firstly, on account of the definitions of \(\psi\)-type stability and \(\psi\)-type function, the concept of decay anti-synchronization is proposed. Then, we investigate the decay anti-synchronization of MWCNNs with and without delayed coupling by designing appropriate nonlinear controllers, and several criteria for ensuring decay anti-synchronization are inferred by means of Lyapunov functional method as well as inequality techniques. Similarly, some conditions for decay anti-synchronization of MWCRDNNs with and without delayed coupling are also, respectively, derived. Lastly, two numerical examples with simulations are given to validate the correctness of these derived results.


General decay anti-synchronization MWCNNs Nonlinear control Delayed coupling Reaction–diffusion terms 



The authors would like to thank the Associate Editor and anonymous reviewers for their valuable comments and suggestions. They also wish to express their sincere appreciation to Prof. Jinliang Wang for the fruitful discussions and valuable suggestions which helped to improve this paper. This work was supported in part by the Natural Science Foundation of Tianjin City under Grant 18JCQNJC74300, in part by the National Natural Science Foundation of China under Grant 61773285, and in part by Chinese Scholarship Council (No. 201808120044). Dr E. Yang is supported in part under the RSE-NNSFC Joint Project (2017–2019) under Grant 6161101383 with China University of Petroleum (East China).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Computer Science and Technology, Tianjin Key Laboratory of Optoelectronic Detection Technology and SystemTianjin Polytechnic UniversityTianjinChina
  2. 2.School of Computer Science and TechnologyTianjin Polytechnic UniversityTianjinChina
  3. 3.Department of Design, Manufacture and Engineering Management, Faculty of EngineeringUniversity of StrathclydeGlasgowUK

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