Skip to main content

On Robust Periodicity of Delayed Dynamical Systems with Time-Varying Parameters

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3173))

Abstract

In this paper, robust exponential periodicity of a class of dynamical systems with time-varying parameters is introduced. Novel robust criteria to ensuring existence and uniqueness of periodic solution for a general class of neural systems are proposed without assuming the smoothness and boundedness of the activation functions. Which one is the best in previous results is addressed.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Driessche, P.V., Zou, X.: Global Attactivity in Delayed Hopfield Neural Network Models. SIAM Journal of Applied Mathematics 58, 1878–1890 (1998)

    Article  MATH  Google Scholar 

  2. Liao, X., Wang, J.: Algebraic Criteria for Global Exponential Stability of Cellular Neural Networks with Multiple Time Delays. IEEE Trans. Circuits Systems I 50, 268–275 (2003)

    Article  MathSciNet  Google Scholar 

  3. Arik, S., Tavsanoglu, V.: Global Robust Stability of Delayed Neural Networks. IEEE Transactions on Circuits and Systems I 50, 156–160 (2003)

    Article  Google Scholar 

  4. Forti, M., Tesi, A.: New Conditions for Global Stability of Neural Networks with Application to Linear and Quadratic Programming Problems. IEEE Trans. Circuits and Systems I 42, 354–366 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  5. Sudharsanan, S., Sundareshan, M.: Exponential Stability and a Systematic Synthesis of a Neural Network for Quadratic Minimization. Neural Networks 4, 599–613 (1991)

    Article  Google Scholar 

  6. Morita, M.: Associative Memory with Non-monntone Dynamics. Neural networks 6, 115–126 (1993)

    Article  Google Scholar 

  7. Tank, D.W., Hopfield, J.: Simple “Neural” Optimization Networks: an A/D Converter, Signal Decision Circuit, and a Linear Programming Circuit. IEEE Trans. Circuits & Systems 33, 533–541 (1986)

    Article  Google Scholar 

  8. Kennedy, M., Chua, L.: Neural Networks for Linear and Nonlinear Programming. IEEE Trans. Circuits & Systems 35, 554–562 (1988)

    Article  MathSciNet  Google Scholar 

  9. Townley, S., Ilchmann, A., Weiss, M., et al.: Existence and Learning of Oscillations in Recurrent Neural Networks. IEEE Trans. Neural Networks 11, 205–214 (2000)

    Article  Google Scholar 

  10. Sun, C., Feng, C.B.: Exponential Periodicity of Continuous-time and Discrete-time Neural Networks with Delays. Neural Processing Letters 19, 131–146 (2004)

    Article  MathSciNet  Google Scholar 

  11. Sun, C., Zhang, K., Fei, S., et al.: On Exponential Stability of Delayed Neural Networks with a General Class of Activation Functions. Physics Letters A 298, 122–132 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  12. Sun, C., Feng, C.B.: Global Robust Exponential Stability of Interval Neural Networks with Delays. Neural Processing Letters 17, 107–115 (2003)

    Article  Google Scholar 

  13. Sun, C., Feng, C.B.: On Robust Exponential Periodicity of Interval Neural Networks with Delays. Neural Processing Letters 20, 1–10 (2004)

    Article  MATH  Google Scholar 

  14. Sun, C., Feng, C.B.: Exponential Periodicity and Stability of Delayed Neural Networks. Mathematics and Computers in Simulation 66, 1–9 (2004)

    Article  MathSciNet  Google Scholar 

  15. Mohamad, S., Gopalsamy, K.: Neuronal Dynamics in Time Varying Environments: Continuous and Discrete Time Models. Discrete and Continuous Dynamical Systems 6, 841–860 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  16. Zhang, Y., Chen, T.: Global Exponential Stability of Delayed Periodic Dynamical System. Physics Letters A 322, 344–355 (2004)

    Article  MathSciNet  Google Scholar 

  17. Liang, X., Wang, J.: Absolute Exponential Stability of Neural Networks with a General Class of Activation Functions. IEEE Transaction on Circuits and Systems: I 47, 1258–1263 (2000)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sun, C., Li, X., Feng, CB. (2004). On Robust Periodicity of Delayed Dynamical Systems with Time-Varying Parameters. In: Yin, FL., Wang, J., Guo, C. (eds) Advances in Neural Networks – ISNN 2004. ISNN 2004. Lecture Notes in Computer Science, vol 3173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28647-9_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-28647-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22841-7

  • Online ISBN: 978-3-540-28647-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics