Skip to main content

Robust Multistability and Multiperiodicity of Neural Networks with Time Delays

  • Conference paper
  • First Online:
Advances in Neural Networks – ISNN 2015 (ISNN 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9377))

Included in the following conference series:

Abstract

In this paper, we are concerned with the robust multistability and multiperiodicity of delayed neural networks. A set of sufficient conditions ensuring the coexistence of 2n periodic solutions and their local stability are presented. And the attraction basin of each periodic solution can be enlarged by rigorous analysis.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arik, S., Tavsanoglu, V.: On the global asymptotic stability of delayed cellular neural networks. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 47(4), 571–574 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen, T., Amari, S.: New theorems on global convergence of some dynamical systems. Neural Networks 14, 251–255 (2001)

    Article  Google Scholar 

  3. Chen, T., Rong, L.: Robust global exponential stability of Cohen-Grossberg neural networks with time delays. IEEE Transactions on Neural Networks 15(1), 203–206 (2004)

    Article  Google Scholar 

  4. Lu, W., Chen, T.: Global exponential stability of almost periodic solution for a large class of delayed dynamical systems. Science in China Series A-Mathematics 48(8), 1015–1026 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Zeng, Z., Wang, J.: Multiperiodicity and exponential attractivity evoked by periodic external inputs in delayed cellular neural networks. Neural Computation 18(4), 848–870 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cheng, C., Lin, K., Shih, C.: Multistability in recurrent neural networks. SIAM Journal on Applied Mathematics 66(4), 1301–1320 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang, L., Yi, Z., Yu, J.: Multiperiodicity and attractivity of delayed recurrent neural networks with unsaturating piecewise linear transfer functions. IEEE Transactions on Neural Networks 19(1), 158–167 (2008)

    Article  Google Scholar 

  8. Wang, L., Lu, W., Chen, T.: Multistability and new attraction basins of almost-periodic solutions of delayed neural networks. IEEE Transactions on Neural Networks 20(10), 1581–1593 (2009)

    Article  Google Scholar 

  9. Wang, L., Lu, W., Chen, T.: Coexistence and local stability of multiple equilibria in neural networks with piecewise linear nondecreasing activation functions. Neural Networks 23, 189–200 (2010)

    Article  MATH  Google Scholar 

  10. Wang, L., Chen, T.: Multiple μ-stability of neural networks with unbounded time-varying delays. Neural Networks 53, 109–118 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lili Wang .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Wang, L. (2015). Robust Multistability and Multiperiodicity of Neural Networks with Time Delays. In: Hu, X., Xia, Y., Zhang, Y., Zhao, D. (eds) Advances in Neural Networks – ISNN 2015. ISNN 2015. Lecture Notes in Computer Science(), vol 9377. Springer, Cham. https://doi.org/10.1007/978-3-319-25393-0_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25393-0_17

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25392-3

  • Online ISBN: 978-3-319-25393-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics