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Adaptive Exponential Synchronization of Stochastic Delay Neural Networks with Reaction-Diffusion

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Advances in Neural Networks – ISNN 2009 (ISNN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5551))

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Abstract

In the paper, adaptive exponential synchronization scheme for a class of reaction-diffusion neural networks with continuously distributed delays and stochastic influence are considered. An adaptive synchronization controller is derived to achieve the exponential synchronization of the drive-response structure of neural networks. Lyapunov stability theory, stochastic Fubini theorem and semimartingale theorem are used in our approach. It is shown that the approaches developed here extend and improve the ideas presented in recent literatures.

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References

  1. Pecora, L.M., Carrol, T.L.: Synchronization in Chaotic Systems. Phys. Rev. Lett. 64, 821–833 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Pecora, L.M., Carrol, T.L., Johnson, G.A.: Fundamentals of Synchronization in Chaotic Systems, Concepts, and Applications. Chaos 7, 520–543 (1998)

    Article  MathSciNet  Google Scholar 

  3. Khadra, A., Liu, X., Shen, X.: Impulsively Synchronizing Chaotic Systems with Delay and Applications to Secure Communication. Automatica 41, 1491–1502 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  4. Wang, Y., Guan, Z., Xiao, J.: Impulsive Control for Synchronization of a Class of Continuous Systems. Chaos 14, 199–203 (2004)

    Article  Google Scholar 

  5. Sun, Y., Cao, J.: Adaptive Lag Synchronization of Unknown Chaotic Delayed Neural Networks with Noise Perturbation. Phys. Lett. A 364, 277–285 (2007)

    Article  MATH  Google Scholar 

  6. Xiong, W., Xie, W., Cao, J.: Adaptive Exponential Synchronization of Delayed Chaotic Networks. Physica A 370, 832–842 (2006)

    Article  Google Scholar 

  7. Sun, J.: Delay-dependent Stability Criteria for Time-delay Chaotic Systems Via Time-delay Feedback Control. Chaos, Solitons & Fractals 21, 143–150 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Cao, J., Li, H., Daniel, W.: Synchronization Criteria of Lure Systems with Time-delay Feedback Control. Chaos, Solitons & Fractals 23, 1285–1298 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Park, J.: A Novel Criterion for Delayed Feedback Control of Time-delay Chaotic Systems. Chaos, Solitons & Fractals 23, 495–501 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Li, Z., Chen, G.: Global Synchronization and Asymptotic Stability of Complex Dynamical Networks. IEEE.Trans. Circuits Syst. 53, 28–33 (2006)

    Article  Google Scholar 

  11. Li, P., Cao, J., Wang, Z.: Robust Impulsive Synchronization of Coupled Delayed Neural Networks with Uncertainties. Physica A 373, 261–272 (2007)

    Article  Google Scholar 

  12. Chen, G., Zhou, J., Liu, Z.: Global Synchronization of Coupled Delayed Neural Networks with Application to Chaotic CNN models. Int. J. Bifurcat. Chaos 14, 2229–2240 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  13. Lu, W., Chen, T.: Synchronization of Coupled Connected Neural Networks with Delays. IEEE. Trans. Circuit Syst. II 51, 2491–2503 (2004)

    Article  MathSciNet  Google Scholar 

  14. Lu, H.T., Van, L.C.: Synchronization of Chaotic Neural Networks Via Output or State Coupling. Chaos, Solitons & Fractals 30, 166–176 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang, Y., Cao, J.: Synchronization of a Class of Delayed Neural Networks with Reaction-Diffusion Terms. Phys Lett. A 369, 201–211 (2007)

    Article  Google Scholar 

  16. Song, Q.K., Zhao, Z.J., Li, Y.M.: Global Exponential Stability of BAM with Distributed Delays and Reaction-diffusion Terms. Phys. Lett. A 335, 213–225 (2005)

    Article  MATH  Google Scholar 

  17. Lou, X., Cui, B.: Boundedness and Exponential Stability for Nonautonomous Cellular Neural Networks with Reaction-diffusion Terms. Chaos, Solitons & Fractals 33, 653–662 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yuan, K., Cao, J., Li, H.: Robust Stability of Switched Cohen-Grossberg Neural Networks with Mixed Time-varying Delays. IEEE Trans. Syst. Man Cybernet – Part B 36, 1356–1363 (2006)

    Article  Google Scholar 

  19. Luo, Q.I., Deng, F.Q., Zhao, B.R.: Stabilization of Stochastic Hopfield Neural Network with Distributed Parameters. Science in China (F) 7, 752–762 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  20. Lv, Y., Lv, W., Sun, J.H.: Convergence Dynamics of Stochastic Reaction–diffusion Recurrent Neural Networks with Continuously Distributed Delays. Nonlinear Analysis: Real World Applications 9, 1590–1606 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  21. Sheng, L., Yang, H.Z., Lou, X.Y.: Adaptive Exponential Synchronization of Delayed Neural Networks with Reaction-diffusion Terms. Chaos, Solitons and Fractals, 1–10 (2007)

    Google Scholar 

  22. Wang, Z., Liu, Y., Liu, X.: On Global asymptotic Stability of Neural Networks with Discrete and Distributed Delays. Phys. Lett. A 345, 299–308 (2005)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics , School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong, 510006, China

    Birong Zhao

  2. Control of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, China

    Feiqi Deng

Authors
  1. Birong Zhao
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  2. Feiqi Deng
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Editor information

Editors and Affiliations

  1. Departamento de Control Automático, CINVESTAV-IPN, A.P. 14-740, Av.IPN 2508, 07360, México D.F., México

    Wen Yu

  2. Deptartment of Electrical and Computer Engineering, Stevens Institute of Technology, NJ 07030, Hoboken, USA

    Haibo He

  3. Dept. of Electrical and Computer Engineering, South Dakota School of Mines & Technology, 501 E. St. Joseph Street, Rapid City, SD 57701, USA

    Nian Zhang

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© 2009 Springer-Verlag Berlin Heidelberg

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Zhao, B., Deng, F. (2009). Adaptive Exponential Synchronization of Stochastic Delay Neural Networks with Reaction-Diffusion. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01507-6_63

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  • DOI: https://doi.org/10.1007/978-3-642-01507-6_63

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01506-9

  • Online ISBN: 978-3-642-01507-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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