Neural Computing and Applications

, Volume 18, Issue 5, pp 515–521 | Cite as

Anti-synchronization of stochastic perturbed delayed chaotic neural networks

ISNN 2008


This paper studies the anti-synchronization of a class of stochastic perturbed chaotic delayed neural networks. By employing the Lyapunov functional method combined with the stochastic analysis as well as the feedback control technique, several sufficient conditions are established that guarantee the mean square exponential anti-synchronization of two identical delayed networks with stochastic disturbances. These sufficient conditions, which are expressed in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. Two numerical examples are exploited to demonstrate the feasibility and applicability of the proposed synchronization approaches.


Chaotic delayed neural networks Anti-synchronization Stochastic perturbation Time delay Feedback control 



This work was jointly supported by the National Natural Science Foundation of China under Grant No. 60874088, the Specialized Research Fund for the Doctoral Program of Higher Education under Grant 20070286003 and the Foundation for Excellent Doctoral Dissertation of Southeast University YBJJ0705.


  1. 1.
    Pecora LM, Carroll TL (1990) Synchronization in chaotic systems. Phys Rev Lett 64(8):821–824CrossRefMathSciNetGoogle Scholar
  2. 2.
    Carroll TL, Pecora LM (1991) Synchronization in chaotic circuits. IEEE Trans Circ Syst 38:453–456CrossRefGoogle Scholar
  3. 3.
    Pecora LM, Carroll TL, Johnson GA (1997) Fundamentals of synchronization in chaotic systems, concepts, and applications. Chaos 7(4):520–543MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Kocarev L, Parlitz U (1996) Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. Phys Rev Lett 76:1816–1819CrossRefGoogle Scholar
  5. 5.
    Yang SS, Duan K (1998) Generalized synchronization in chaotic systems. Chaos Solitons Fractals 10:1703–1707CrossRefMathSciNetGoogle Scholar
  6. 6.
    Michael GR, Arkady SP, Jürgen K (1996) Phase synchronization of chaotic oscillators. Phys Rev Lett 76:1804–1807CrossRefGoogle Scholar
  7. 7.
    Taherion IS, Lai YC (1999) Observability of lag synchronization of coupled chaotic oscillators. Phys Rev E 59:6247–6250CrossRefGoogle Scholar
  8. 8.
    Zhang Y, Sun J (2004) Chaotic synchronization and anti-synchronization based on suitable separation. Phys Lett A 330:442–447MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Li GH (2005) Synchronization and anti-synchronization of colpitts oscillators using active control. Chaos Solitons Fractals 26:87–93MATHCrossRefGoogle Scholar
  10. 10.
    Li GH, Zhou SP (2006) An observer-based anti-synchronization. Chaos Solitons Fractals 29:495–498MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Miller DA, Kowalski KL, Lozowski A (1999) Synchronization and anti-synchronization of Chuas oscillators via a piecewise linear coupling Circuit. In: Proceedings fo the 1999 IEEE international symposium on circuit systems, ISCAS99. 5:458–462 (unpublished)Google Scholar
  12. 12.
    Wedekind I, Parlitz U (2001) Experimental observation of synchronization and anti-synchronization of chaotic low-frequency-fluctuations in external cavity semiconductor lasers. Int J Bifurcation Chaos Appl Sci Eng 11:1141–1147CrossRefGoogle Scholar
  13. 13.
    Kim CM, Rim SW, Key W et al (2003) Anti-synchronization of chaotic oscillators. Phys Lett A 320:39–46MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Hu G, Pivka L, Zheleznyak A (1995) Synchronization of a one-dimensional array of Chua’s circuits by feedback control and noise. IEEE Trans Circuits Syst I 42:736–740CrossRefGoogle Scholar
  15. 15.
    Sáchez E, Matías M, Muñuzuri V (1997) Analysis of synchronization of chaotic systems by noise: an experimental study. Phys Rev E 56:4068–4071CrossRefGoogle Scholar
  16. 16.
    Wang M, Hou Z, Xin H (2005) Internal noise-enhanced phase synchronization of coupled chemical chaotic oscillators. J Phys A 38:145–152MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Yu WW, Cao JD (2007) Robust control of uncertain stochastic recurrent neural networks with time-varying delay. Neural Process Lett 26(2):101–119CrossRefMathSciNetGoogle Scholar
  18. 18.
    Sun YH, Cao JD, Wang ZD (2007) Exponential synchronization of stochastic perturbed chaotic delayed neural networks. Neurocomputing 70(13–15):2477–2485CrossRefGoogle Scholar
  19. 19.
    Meng J, Wang XY (2007) Robust anti-synchronization of a class of delayed chaotic neural networks. Chaos 17:023113CrossRefMathSciNetGoogle Scholar
  20. 20.
    Friedman A (1976) Stochastic differential equations and applications. Academic Press, New YorkMATHGoogle Scholar
  21. 21.
    Baker C, Buckwar E (2005) Exponential stability in p-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay diffrential equations. J Comput Appl Math 184:404–427MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Boyd S, Ghaoui LE, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiaMATHGoogle Scholar
  23. 23.
    Arnold L (1974) Stochastic differential equations: theory and applications. Wiley, LondonMATHGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2009

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjingChina

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