Neural Processing Letters

, Volume 42, Issue 2, pp 501–515 | Cite as

Synchronization Analysis of Coupled Stochastic Neural Networks with On–Off Coupling and Time-Delay

  • Guan Wang
  • Yi Shen
  • Quan Yin


In this paper, synchronization problem of coupled neural networks with stochastic disturbances and time-delay is analyzed. For the system under study, each subsystem interacts with others in an on–off way which can be employed to deal with communication congestion in signals transmission. By stochastic analysis techniques, sufficient conditions that guarantee mean square synchronization of the coupled system are established. Moreover, the underlying network needs not be undirected or strongly connected. Finally, some numerical simulations are given to verify the usefulness and effectiveness of our results.


Synchronization Coupled neural networks On–off coupling Stochastic disturbances 



The authors gratefully acknowledge anonymous referees’ comments and patient work. This work is supported by the National Science Foundation of China under Grant No. 11271146 and the Key Program of National Natural Science Foundation of China under Grant No. 61134012 and the Key Program of Wuhan under Grant No. 2013010501010117.


  1. 1.
    Chang C, Fan K, Chung I, Lin C (2006) A recurrent fuzzy coupled cellular neural network system with automatic structure and template learning. IEEE Trans Circuits Syst Express Briefs 53:602–606CrossRefGoogle Scholar
  2. 2.
    Chua L, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circuits Syst 35:1257–1272MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Karimi H, Gao H (2010) New delay-dependent exponential \(H_{\infty }\) synchronization for uncertain neural networks with mixed time delays. IEEE Trans Syst Man Cybern Part B 40:173–185CrossRefMATHGoogle Scholar
  4. 4.
    Cao J, Chen G, Li P (2008) Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Trans Syst Man Cybern Part B 38:488–498CrossRefGoogle Scholar
  5. 5.
    Zhang H, Wang Y (2008) Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 19:366–370CrossRefGoogle Scholar
  6. 6.
    Liang J, Wang Z, Liu Y, Liu X (2008) Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks. IEEE Trans Neural Netw 19:1910–1920CrossRefGoogle Scholar
  7. 7.
    Shen Y, Wang J (2007) Noise-induced stabilization of the recurrent neural networks with mixed time-varying delays and Markovian-switching parameters. IEEE Trans Neural Netw 18:1857–1862CrossRefGoogle Scholar
  8. 8.
    Shen Y, Wang J (2009) Almost sure exponential stability of recurrent neural networks with Markovian switching. IEEE Trans Neural Netw 20:840–855CrossRefGoogle Scholar
  9. 9.
    Liu Y, Wang Z, Liang J, Liu X (2009) Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays. IEEE Trans Neural Netw 20:1102–1116CrossRefGoogle Scholar
  10. 10.
    Liu Y, Wang Z, Liu X (2009) On global stability of delayed BAM stochastic neural networks with Markovian switching. Neural Process Lett 30:19–35CrossRefGoogle Scholar
  11. 11.
    Lu J, Ho D, Wang Z (2009) Pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers. IEEE Trans Neural Netw 20:1617–1629CrossRefMATHGoogle Scholar
  12. 12.
    Suganthan P, Teoh E, Mital D (1995) Pattern recognition by homomorphic graph matching using Hopfield neural networks. Image Vis Comput 13:45–60CrossRefGoogle Scholar
  13. 13.
    Zhang H, Liu Z, Huang G, Wang Z (2010) Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay. IEEE Trans Neural Netw 21:91–106CrossRefGoogle Scholar
  14. 14.
    Wu A, Zeng Z (2012) Exponential stabilization of memristive neural networks with time delays. IEEE Trans Neural Netw Learn Syst 23:1919–1929CrossRefMATHGoogle Scholar
  15. 15.
    Zhang H, Ma T, Huang G, Wang Z (2010) Robust global exponential synchronization of uncertain chaotic delayed neural networks via dual-stage impulsive control. IEEE Trans Syst Man Cybern Part B Cybern 40:831–844CrossRefGoogle Scholar
  16. 16.
    Yang X, Cao J, Lu J (2012) Synchronization of Markovian coupled neural networks with nonidentical node-delays and random coupling strengths. IEEE Trans Neural Netw Learn Syst 23:60–71MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zhang H, Gong D, Wang Z, Ma D (2012) Synchronization criteria for an array of neutral-type neural networks with hybrid coupling: a novel analysis approach. Neural Process Lett 35:29–45CrossRefGoogle Scholar
  18. 18.
    Xia Y, Yang Z, Han M (2009) Lag synchronization of unknown chaotic delayed Yang-Yang-Type fuzzy neural networks with noise perturbation based on adaptive control and parameter identification. IEEE Trans Neural Netw 20:1165–1180CrossRefMATHGoogle Scholar
  19. 19.
    Zeng Z, Wang J (2009) Associative memories based on continuous-time cellular neural networks designed using space-invariant cloning templates. Neural Netw 22:651–657CrossRefGoogle Scholar
  20. 20.
    Zhu S, Shen Y (2011) Passivity analysis of stochastic delayed neural networks with Markovian switching. Neurocomputing 74:1754–1761CrossRefMATHGoogle Scholar
  21. 21.
    Zhang G, Shen Y, Sun J (2012) Global exponential stability of a class of memristor-based recurrent neural networks with time-varying delays. Neurocomputing 97:149–154CrossRefGoogle Scholar
  22. 22.
    Kadji H, Orou J, Woafo P (2008) Synchronization dynamics in a ring of four mutually coupled biological systems. Commun Nonlinear Sci Numer Simul 13:1361–1372MathSciNetCrossRefGoogle Scholar
  23. 23.
    Massimiliano D, Mario D, Edmondo D, Sabato M (2012) Synchronization of networks of non-identical chua’s circuits: analysis and experiments. IEEE Trans Circuits Syst Regul Pap 59:1029–1041CrossRefGoogle Scholar
  24. 24.
    Wu C, Chua L (1995) Synchronization in an array of linearly coupled dynamical systems. IEEE Trans Circuits Syst I Fundam Theor Appl 42:430–447MathSciNetCrossRefGoogle Scholar
  25. 25.
    Liu H, Lu J, Lü J, Hill D (2009) Structure identification of uncertain general complex dynamical networks with time delay. Automatica 45:1799–1807CrossRefMATHGoogle Scholar
  26. 26.
    Wu C (2010) Evolution and dynamics of complex networks of coupled systems. IEEE Circuits Syst Mag 10:55–63CrossRefGoogle Scholar
  27. 27.
    Wang Z, Wang Y, Liu Y (2010) Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays. IEEE Trans Neural Netw 21:11–25CrossRefGoogle Scholar
  28. 28.
    Lü J, Chen G (2005) A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans Autom Control 50:841–846CrossRefGoogle Scholar
  29. 29.
    Qin B, Lu X (2010) Adaptive approach to global synchronization of directed networks with fast switching topologies. Phys Lett A 374:3942–3950CrossRefGoogle Scholar
  30. 30.
    Chen L, Qiu C, Huang H (2009) Synchronization with on–off coupling: role of time scales in network dynamics. Phys Rev E 79:045101CrossRefGoogle Scholar
  31. 31.
    Lü J, Yu X, Chen G, Cheng D (2004) Characterizing the synchronizability of small-world dynamical networks. IEEE Trans Circuits Syst Regul Pap 51:787–796CrossRefGoogle Scholar
  32. 32.
    Yang M, Wang Y, Xiao J, Wang H (2010) Robust synchronization of impulsively-coupled complex switched networks with parametric uncertainties and time-varying delays. Nonlinear Anal Real World Appl 11:3008–3020MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Langville A, Stewart W (2004) The Kronecker product and stochastic automata networks. J Comput Appl Math 167:429–447MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Chen B, Chiang C, Nguang S (2011) Robust \(H_{\infty }\) synchronization design of nonlinear coupled network via fuzzy interpolation method. IEEE Trans Circuits Syst Regul Pap 58:349–362MathSciNetCrossRefGoogle Scholar
  35. 35.
    Wu W, Zhou W, Chen T (2009) Cluster synchronization of linearly coupled complex networks under pinning control. IEEE Trans Circuits Syst Regul Pap 56:829–839MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Li C, Liao X, Huang T (2007) Exponential stabilization of chaotic systems with delay by periodically intermittent control. Chaos 17:013103MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.School of AutomationHuazhong University of Science and TechnologyWuhanChina
  2. 2.Key Laboratory of Image Processing and Intelligent Control of Education Ministry of ChinaWuhanChina

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