Neural Processing Letters

, Volume 49, Issue 1, pp 141–157 | Cite as

Pinning Synchronization of Nonlinear and Delayed Coupled Neural Networks with Multi-weights via Aperiodically Intermittent Control

  • Chengbo Yi
  • Jianwen FengEmail author
  • Jingyi WangEmail author
  • Chen Xu
  • Yi Zhao
  • Yanhong Gu


This paper deals with the synchronization issues of delayed neural networks with multi-weights under aperiodically intermittent pinning control. There are three main differences of this paper with previous works: firstly, aperiodically intermittent pinning control scheme is used to synchronize the proposed neural networks; secondly, the model is delayed neural networks with multi-weights, which have several different sorts of weights between two nodes; thirdly, internal delay and multi-coupling delays are considered simultaneously. By establishing new nonlinear inequalities and constructing Lyapunov function, several sufficient criteria are derived to guarantee exponential synchronization for the proposed neural network models. Moreover, an effective pinned-node selection scheme which determines what kind of nodes should be prior controlled is provided. Finally, two illustrative examples are presented to demonstrate the effectiveness of the theoretical results.


Synchronization Delayed neural networks Multi-weights Aperiodically Intermittent pinning 



The authors would like to thank the associate editor and the anonymous reviewers for their insightful suggestions. This work was supported in parts by the National Natural Science Foundation of China under Grants 61472257, 61603260 and 61273220, and the Postdoctoral Science Foundation of China under Grant 2016M590811.


  1. 1.
    Wang J, Feng J, Xu C, Michael C, Zhao Y, Feng J (2016) The synchronization of instantaneously coupled harmonic oscillators using sampled data with measurement noise. Automatica 66:155–162MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Pecora L, Carroll T (1998) Master stability functions for synchronized coupled systems. Phys Rev Lett 80:2109–2112CrossRefGoogle Scholar
  3. 3.
    Perez-Munuzuri V, Perez-Villar V, Chua L (1993) Autowaves for image processing on a two-dimensional CNN array of excitible nonlinear circuits: flat and wrinkled labyrinths. IEEE Trans Circuits Syst I 40:174–181CrossRefzbMATHGoogle Scholar
  4. 4.
    Yang X, Lu J (2016) Finite-time synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans Autom Control 61:2256–2261MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Xie Q, Chen G, Bollt E (2002) Hybrid chaos synchronization and its application in information processing. Math Comput Model 35:145–163MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Yang X, Feng Z, Feng J, Cao J (2017) Synchronization of discrete-time neural networks with delays and Markov jump topologies based on tracker information. Neural Netw 85:157–164CrossRefGoogle Scholar
  7. 7.
    Cao J, Chen G, Li P (2008) Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Tran Syst Man Cybern Part B Cybern A Publ IEEE Syst Man Cybern Soc 38:488–98CrossRefGoogle Scholar
  8. 8.
    Cao J, Li L (2009) Cluster synchronization in an array of hybrid coupled neural networks with delay. Neural Netw 22:335–342CrossRefzbMATHGoogle Scholar
  9. 9.
    Li Y, Li X, Ouyang G, Guan X (2005) Strength and direction of phase synchronization of neural networks. Int Conf Adv Neural Netw 20:314–319zbMATHGoogle Scholar
  10. 10.
    Hu C, Yu J, Jiang H, Teng Z (2010) Exponential lag synchronization for neural networks with mixed delays via periodically intermittent control. Chaos Interdiscip J Nonlinear Sci 20:20023108MathSciNetzbMATHGoogle Scholar
  11. 11.
    Yang X, Ho Daniel W C, Lu J, Song Q (2015) Finite-time cluster synchronization of T-S fuzzy complex networks with discontinuous subsystems and random coupling delays. IEEE Trans Fuzzy Syst 23:2302–2316CrossRefGoogle Scholar
  12. 12.
    Yang X, Song Q, Liang J, He B (2015) Finite-time synchronization of coupled discontinuous neural networks with mixed delays and nonidentical perturbations. J Frankl Inst 352:4382–4406MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Wang H, Li X (2001) Optimal analysis of the path of the network with double weights. J Jilin Inst Chem Technol 18:64–66Google Scholar
  14. 14.
    An X, Zhang L, Li Y (2014) Synchronization analysis of complex networks with multi-weights and its application in public traffic network. Phys A Stat Mech Appl 412:149–156MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Cao Y, Zhao X (2004) Data fitting based on a new double weights neural network. Acta Electron Sin 32:1671–1673Google Scholar
  16. 16.
    Zhang Y, Cheng W (2012) An optimized application based on double-weight neural network and genetic algorithm. Inf Bus Intell 53:2001–2004Google Scholar
  17. 17.
    Chen T, Liu X, Lu W (2007) Pinning complex networks by a single controller. IEEE Trans Circuits Syst I Regul Pap 54:1317–1326MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Zhou J, Wu Q, Xiang L (2012) Impulsive pinning complex dynamical networks and applications to firing neuronal synchronization. Nonlinear Dyn 69:1393–1403MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Yu W, Chen G, Lü J, Kurths J (2013) Synchronization via pinning control on general complex networks. SIAM J Control Optim 51:1395–1416MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Song Q, Cao J, Liu F (2012) Pinning-controlled synchronization of hybrid-coupled complex dynamical networks with mixed time-delays. Int J Robust Nonlinear Control 22:690–706MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Guan Z, Hill D, Shen X (2005) On hybrid impulsive and switching systems and application to nonlinear control. IEEE Trans Autom Control 50:1058–1062MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Yang X, Cao J, Lu J (2011) Synchronization of delayed complex dynamical networks with impulsive and stochastic effects. Nonlinear Anal Real World Appl 12:2252–2266MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Wang B, Guan Z (2010) Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans Circuits Syst I Regular Pap 57:2182–2195MathSciNetCrossRefGoogle Scholar
  24. 24.
    Feng J, Yu F, Zhao Y (2016) Exponential synchronization of nonlinearly coupled complex networks with hybrid time-varying delays via impulsive ontrol. Nonlinear Dyn 85:621–632CrossRefzbMATHGoogle Scholar
  25. 25.
    Liu Y, Guo B, Park J, Lee S (2016) Nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled-data control. IEEE Trans Neural Netw Learn Syst 99:1–11Google Scholar
  26. 26.
    Cai S, Zhou P, Liu Z (2014) Pinning synchronization of hybrid-coupled directed delayed dynamical network via intermittent control. Chaos 24:268–2622MathSciNetzbMATHGoogle Scholar
  27. 27.
    Huang T (2008) Synchronization of coupled system by intermittent control. For Ecol Manag 259:71–80Google Scholar
  28. 28.
    Feng J, Yang P, Zhao Y (2016) Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control. Appl Math Comput 291:52–68MathSciNetzbMATHGoogle Scholar
  29. 29.
    Liu X, Li P, Chen T (2015) Cluster synchronization for delayed complex networks via periodically intermittent pinning control. Neurocomputing 162:191–200CrossRefGoogle Scholar
  30. 30.
    Wang S, Jiang M, Mei J, Han J (2013) Exponential topology identification of general complex networks with time-varying delay via periodically intermittent control. Int Conf Intell Hum Mach Syst Cybern IEEE 1:513–516Google Scholar
  31. 31.
    Wang J, Feng J, Xu C, Zhao Y (2013) Exponential synchronization of stochastic perturbed complex networks with time-varying delays via periodically intermittent pinning. Commun Nonlinear Sci Numer Simul 18:3146–3157MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Liu M, Jiang H, Hu C (2016) Synchronization of hybrid-coupled delayed dynamical networks via aperiodically intermittent pinning control. J Frankl Inst 353:2722–2742MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Liu X, Chen T (2005) Synchronization of complex networks via aperiodically intermittent pinning control. IEEE Trans Autom Control 60:3316–3321MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Wang J (2016) Synchronization of delayed complex dynamical network with hybrid-coupling via aperiodically intermittent pinning control. J Frankl Inst 354:1833–1855MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Halanay A (1966) Differential equations: Stability, oscillations, time lags. Siam Rev 10:93–94zbMATHGoogle Scholar
  36. 36.
    Liu B, Lu W, Chen T (2014) New criterion of asymptotic stability for delay systems with time-varying structures and delays. Neural Netw 54:103–111CrossRefzbMATHGoogle Scholar
  37. 37.
    An X, Zhang L, Zhang J (2015) Research on urban public traffic network with multi-weights based on single bus transfer junction. Physica A Stat Mech Appl 436:748–755MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Mathematics and StatisticsShenzhen UniversityShenzhenPeople’s Republic of China

Personalised recommendations