Skip to main content
SpringerLink
Log in

Robust Stability and Synchronization of Neural Networks

  • Chapter
  • First Online:
Stability and Synchronization Control of Stochastic Neural Networks

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 35))

  • 1101 Accesses

Abstract

In this chapter, the robust stability of high-order neural networks and hybrid stochastic neural networks is first investigated. The robust anti-synchronization and robust lag synchronization of chaotic neural networks are discussed in the sequel.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A. Arenas, A. Guilera, J. Kurths, Y. Morenob, C. Zhoug, Synchronization in complex networks. Phys. Rep. 469(3), 93–153 (2008)

    Article  MathSciNet  Google Scholar 

  2. S. Arik, Global robust stability analysis of neural networks with discrete time delays. Chaos Solitons Fractals 26(5), 1407–1414 (2005)

    Article  MathSciNet  Google Scholar 

  3. L. Arnold, Stochastic Differential Equations: Theory and Applications (Wiley, New York, 1972)

    Google Scholar 

  4. E. Artyomov, O. Yadid-Pecht, Modified high-order neural network for invariant pattern recognition. Pattern Recognit. Lett. 26(6), 843–851 (2005)

    Article  Google Scholar 

  5. W. Baoyun, H. Zenya, N. Jingnan, To implement the CDMA multiuser detector by using transiently chaotic neural network. IEEE Trans. Aerosp. Electron. Syst. 33(3), 1068–1071 (1997)

    Article  Google Scholar 

  6. S. Blythe, X. Mao, X. Liao, Stability of stochastic delay neural networks. J. Frankl. Inst. 338(4), 481–495 (2001)

    Article  MathSciNet  Google Scholar 

  7. S. Boccaletti, V. Latora, Y. Moreno, M. Chevez, D.U. Hwqng, Complex networks: structure and dynamics. Phys. Rep. 424(4–5), 175–308 (2006)

    Article  MathSciNet  Google Scholar 

  8. J. Cao, T. Chen, Globally exponentially robust stability and periodicity of delayed neural networks. Chaos Solitons Fractals 22(4), 957–963 (2004)

    Article  MathSciNet  Google Scholar 

  9. J. Cao, X. Li, Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach. Phys. D 212(1), 54–65 (2005)

    Article  MathSciNet  Google Scholar 

  10. J. Cao, J. Liang, J. Lam, Exponential stability of high-order bidirectional associative memory neural networks with time delays. Phys. D: Nonlinear Phenom. 199(3), 425–436 (2004)

    Article  MathSciNet  Google Scholar 

  11. J. Cao, D. Huang, Y. Qu, Global robust stability of delayed recurrent neural networks. Chaos Solitons Fractals 23(1), 221–229 (2005)

    Article  MathSciNet  Google Scholar 

  12. J. Cao, P. Li, W. Wang, Global synchronization in arrays of delayed neural networks with constant and delayed coupling. Phys. Lett. A 353(4), 318–325 (2006)

    Article  Google Scholar 

  13. J. Cao, Z. Wang, Y. Sun, Synchronization in an array of linearly stochastically coupled networks with time-delays. Phys. A: Stat. Mech. Appl. 385(2), 718–728 (2007)

    Article  MathSciNet  Google Scholar 

  14. J. Cao, G. Chen, P. Li, Global synchronization in an array of delayed neural networks with hybrid coupling. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 38(2), 488–498 (2008)

    Article  MathSciNet  Google Scholar 

  15. S. Celikovsky, V. Lynnyk, Efficient chaos shift keying method based on the second error derivative anti-synchronization detection, in IEEE International Conference on Control and Automation (2009), pp. 530–535

    Google Scholar 

  16. F. Chen, W. Zhang, LMI criteria for robust chaos synchronization of a class of chaotic systems. Nonlinear Anal. Theory Methods Appl. 67(12), 3384–3393 (2007)

    Article  Google Scholar 

  17. G.R. Chen, J. Zhou, Z.R. Liu, Global synchronization of coupled delayed neural networks and applications to chaotic CNN model. Int. J. Bifurc. Chaos 14(7), 2229–2240 (2004)

    Article  MathSciNet  Google Scholar 

  18. A. Dembo, O. Farotimi, T. Kailath, High-order absolutely stable neural networks. IEEE Trans. Circuits Syst. 38(1), 57–65 (1991)

    Article  Google Scholar 

  19. A. Friedman, Stochastic Differential Equations and Their Applications (Academic Press, New York, 1976)

    Google Scholar 

  20. J. Hale, Theory of Functional Differential Equations (Springer, New York, 1977)

    Book  Google Scholar 

  21. Y. He, Q. Wang, M. Wu, C. Lin, Delay-dependent state estimation for delayed neural networks. IEEE Trans. Neural Netw. 17(4), 1077–1081 (2006)

    Article  Google Scholar 

  22. H. Huang, D.W.C. Ho, J. Lam, Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays. IEEE Trans. Circuits Syst.: Part II 52(5), 251–255 (2005)

    Article  Google Scholar 

  23. H. Huang, D.W.C. Ho, Y. Qu, Robust stability of stochastic delayed additive neural networks with Markovian switching. Neural Netw. 20(7), 799–809 (2007)

    Article  Google Scholar 

  24. G. Joya, M. Atencia, F. Sandoval, Hopfield neural networks for optimization: study of the different dynamics. Neurocomputing 43(1), 219–237 (2002)

    Article  Google Scholar 

  25. N.B. Karayiannis, A.N. Venetsanopoulos, On the training and performance of high-order neural networks. Math. Biosci. 129(2), 143–168 (1995)

    Article  Google Scholar 

  26. W. Li, T. Lee, Hopfield neural networks for affine invariant matching. IEEE Trans. Neural Netw. 12(6), 1400–1410 (2001)

    Article  Google Scholar 

  27. X. Liao, G. Chen, E.N. Sanchez, Delay dependent exponential stability analysis of delayed neural networks: an LMI approach. Neural Netw. 15(7), 855–866 (2002)

    Article  MathSciNet  Google Scholar 

  28. M. Li, W. Zhou, H. Wang, Y. Chen, R. Lu, H. Lu, Delay-dependent robust \({H}_\infty \) control for uncertain stochastic systems, in Proceedings of the 17th World Congress of the International Federation of Automatic Control, vol. 17 (2008), pp. 6004–6009

    Google Scholar 

  29. X. Lou, B. Cui, Synchronization of neural networks based on parameter identification and via output or state coupling. J. Comput. Appl. Math. 222(2), 440–457 (2008)

    Article  MathSciNet  Google Scholar 

  30. H. Lu, Comments on “a generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks”. IEEE Trans. Neural Netw. 16(3), 778–779 (2005)

    Article  Google Scholar 

  31. W. Lu, T. Chen, Synchronization of coupled connected neural networks with delays. IEEE Trans. Circuits Syst. I. 51(12), 2491–2503 (2004)

    Article  MathSciNet  Google Scholar 

  32. P. Lu, Y. Yang, Global asymptotic stability of a class of complex networks via decentralised static output feedback control. IET Control Theory Appl. 4(11), 2463–2470 (2010)

    Article  MathSciNet  Google Scholar 

  33. J. Lv, X. Yu, G. Chen, Chaos synchronization of general complex dynamical networks. Phys. A 334(1–2), 281–302 (2004)

    MathSciNet  Google Scholar 

  34. X. Mao, Stochastic Differential Equations and Their Applications (Horwood, Chichester, 1997)

    Google Scholar 

  35. L.M. Pecora, T.L. Carroll, Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  36. D. Psaltis, C. Park, J. Hong, Higher order associative memories and their optical implementations. Neural Netw. 1(2), 143–163 (1988)

    Article  Google Scholar 

  37. F. Ren, J. Cao, LMI-based criteria for stability of high-order neural networks with time-varying delay. Nonlinear Anal. Ser. B: Real World Appl. 7(5), 967–979 (2006)

    Article  MathSciNet  Google Scholar 

  38. F. Ren, J. Cao, Anti-synchronization of stochastic perturbed delayed chaotic neural networks. Neural Comput. Appl. 18(5), 515–521 (2009)

    Article  MathSciNet  Google Scholar 

  39. M.G. Rosenblum, A.S. Pikovsky, J. Kurths, Phase synchronization in driven and coupled chaotic oscillators. IEEE Trans. Circuits Syst. 44(10), 874–881 (1997)

    Article  MathSciNet  Google Scholar 

  40. S. Ruan, R. Filfil, Dynamics of a two-neuron system with discrete and distributed delays. Phys. D 191(3), 323–342 (2004)

    Article  MathSciNet  Google Scholar 

  41. A.N. Ruiz Oliveras, F.R. Pisarchik, Optical chaotic communication using generalized and complete synchronization. IEEE J. Quantum Electron. 46(3), 279–284 (2010)

    Google Scholar 

  42. L. Sheng, M. Gao, Adaptive hybrid lag projective synchronization of unified chaotic systems, in Proceedings of the 29th Chinese Control Conference (2010), pp. 2097–2101

    Google Scholar 

  43. L. Sheng, H. Yang, Robust synchronization of a class of uncertain chaotic neural networks, in 7th World Congress on Intelligent Control and Automation (2008), pp. 4614–4618

    Google Scholar 

  44. S.H. Strogatz, Exploring complex networks. Nature 410(6825), 268–276 (2001)

    Article  Google Scholar 

  45. Y. Tang, R. Qiu, J. Fang, Q. Miao, M. Xia, Adaptive lag synchronization in unknown stochastic chaotic neural networks with discrete and distributed time-varying delays. Phys. Lett. A 372(24), 4425–4433 (2008)

    Article  MathSciNet  Google Scholar 

  46. W. Wang, J. Cao, Synchronization in an array of linearly coupled networks with time-varying delay. Phys. A 366, 197–211 (2006)

    Article  Google Scholar 

  47. Z. Wang, Y. Liu, X. Liu, On global asymptotic stability of neural networks with discrete and distributed delays. Phys. Lett. A 345(4), 299–308 (2005)

    Article  Google Scholar 

  48. Z. Wang, Y. Liu, F. Karl, X. Liu, Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys. Lett. A 354(4), 288–297 (2006)

    Article  Google Scholar 

  49. Z. Wang, Y. Liu, L. Liu, X. Liu, Exponential stability of delayed recurrent neural networks with Markovian jumping parameters. Phys. Lett. A 356(4), 346–352 (2006)

    Article  Google Scholar 

  50. L. Wan, J. Sun, Mean square exponential stability of stochastic delayed Hopfield neural networks. Phys. Lett. A 343(4), 306–318 (2005)

    Article  Google Scholar 

  51. Z. Wang, H. Shu, J. Fang, X. Liu, Robust stability for stochastic Hopfield neural networks with time delays. Nonlinear Anal. Real World Appl. 7(5), 1119–1128 (2006)

    Article  MathSciNet  Google Scholar 

  52. Z. Wang, H. Shu, Y. Liu, D.W.C. Ho, X. Liu, Robust stability analysis of generalized neural networks with discrete and distributed time delays. Chaos Solitons Fractals 30(4), 886–896 (2006)

    Article  MathSciNet  Google Scholar 

  53. Z. Wang, S. Lauria, J. Fang, X. Liu, Exponential stability of uncertain stochastic neural networks with mixed time-delays. Chaos Solitons Fractals 32(1), 62–72 (2007)

    Article  MathSciNet  Google Scholar 

  54. D. Wang, Y. Zhong, S. Chen, Lag synchronizing chaotic system based on a single controller. Commun. Nonlinear Sci. Numer. Simul. 13(3), 637–644 (2008)

    Article  MathSciNet  Google Scholar 

  55. K. Wang, Z. Teng, H. Jiang, Adaptive synchronization of neural networks with time-varying delay and distributed delay. Phys. A: Stat. Mech. Appl. 387(2–3), 631–642 (2008)

    Article  Google Scholar 

  56. L. Wang, W. Liu, H. Shi, Noise chaotic neural networks with variable thresholds for the frequency assignment problem in satellite communications. IEEE Trans. Syst. Man Cybern. Part C: Appl. Rev. 38(2), 209–217 (2008)

    Article  Google Scholar 

  57. Z. Wang, J. Fang, X. Liu, Global stability of stochastic high-order neural networks with discrete and distributed delays. Chaos Solitons Fractals 36(2), 388–396 (2008)

    Article  MathSciNet  Google Scholar 

  58. Z. Wu, H. Su, J. Chu, W. Zhou, Improved result on stability analysis of discrete stochastic neural networks with time delay. Phys. Lett. A 373(17), 1546–1552 (2009)

    Article  MathSciNet  Google Scholar 

  59. Z. Wu, H. Su, J. Chu, W. Zhou, New results on robust exponential stability for discrete recurrent neural networks with time-varying delays. Neurocomputing 72(13), 3337–3342 (2009)

    Article  Google Scholar 

  60. L. Xie, Output feedback \({H}_\infty \) control of systems with parameter uncertainty. Int. J. Control 63(4), 741–750 (1996)

    Article  Google Scholar 

  61. Y. Xu, S. He, Fourier series chaotic neural networks, in Advanced Intelligent Computing Theories and Applications. With Aspects of Contemporary Intelligent Computing Techniques (2008), pp. 84–91

    Google Scholar 

  62. L. Yan, L. Wang, Applications of transiently chaotic neural networks to image restoration, in Proceedings of the 2003 International Conference on Neural Networks and Signal Processing, vol. 1 (2003), pp. 265–269

    Google Scholar 

  63. S. Yong, P. Scott, N. Nasrabadi, Object recognition using multilayer Hopfield neural network. IEEE Trans. Image Process. 6(3), 357–372 (1997)

    Article  Google Scholar 

  64. W. Yu, J. Cao, Synchronization control of stochastic delayed neural networks. Phys. A 373, 252–260 (2007)

    Article  Google Scholar 

  65. H. Zhao, Existence and global attractivity of almost periodic solution for cellular neural network with distributed delays. Appl. Math. Comput. 154(3), 683–695 (2004)

    Article  MathSciNet  Google Scholar 

  66. Y. Zhang, Z. He, A secure communication scheme based on cellular neural networks, in Proceedings of the IEEE International Conference on Intelligent Process Systems, vol. 1 (1997), pp. 521–524

    Google Scholar 

  67. Q. Zhang, X. Wen, J. Xu, Delay-dependent exponential stability of cellular neural networks with time-varying delays. Chaos Solitons Fractals 23(4), 1363–1369 (2005)

    Article  MathSciNet  Google Scholar 

  68. W. Zhou, Y. Xu, H. Lu, L. Pan, On dynamics analysis of a new chaotic attractor. Phys. Lett. A 372(36), 5773–5777 (2008)

    Article  MathSciNet  Google Scholar 

  69. W. Zhou, H. Lu, C. Duan, Exponential stability of hybrid stochastic neural networks with mixed time delays and nonlinearity. Neurocomputing 72(13), 3357–3365 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Sciences and Technology, Donghua University, Shanghai, China

    Wuneng Zhou & Liuwei Zhou

  2. Anyang Normal University, Anyang, China

    Jun Yang

  3. Shanghai University of Engineering Science, Shanghai, China

    Dongbing Tong

Authors
  1. Wuneng Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liuwei Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dongbing Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wuneng Zhou .

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Zhou, W., Yang, J., Zhou, L., Tong, D. (2016). Robust Stability and Synchronization of Neural Networks. In: Stability and Synchronization Control of Stochastic Neural Networks. Studies in Systems, Decision and Control, vol 35. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47833-2_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-47833-2_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47832-5

  • Online ISBN: 978-3-662-47833-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation