Advertisement

Convergence and Periodicity of Solutions for a Class of Discrete-Time Recurrent Neural Network with Two Neurons

  • Hong Qu
  • Zhang Yi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3971)

Abstract

Multistable neural networks have attracted much interesting in recent years, since the monostable networks are computationally restricted. This paper studies a class of discrete-time two-neurons networks with unsaturating piecewise linear activation functions. Some interesting results for the convergence and the periodicity of solutions of the system are obtained.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yi, Z., Wang, P.A., Fu, A.W.C.: Estimate of Exponential Convergence Rate and Exponential Stability for Neural Networks. IEEE Trans. Neural Networks 10(6), 1487–1493 (1999)CrossRefGoogle Scholar
  2. 2.
    Yi, Z., Wang, P.A., Vadakkepat, P.: Absolute Periodicity and Absolute Stability of Delayed Neural Networks. IEEE Trans. Circuits Syst. I 49(2), 256–261 (2002)CrossRefGoogle Scholar
  3. 3.
    Yi, Z., Tan, K.K.: Dynamic Stability Conditions for Lotka-Volterra Recurrent Neural Networks With Delays. Phys. Rev. E 66(1), 11910 (2002)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Hahnloser, R.L.T.: On the Piecewise Analysis of Networks of Linear Threshold Neurons. Neural Networks 11, 691–697 (1998)CrossRefGoogle Scholar
  5. 5.
    Yi, Z., Tan, K.K., Lee, T.H.: Multistability Analysis for Recurrent Neural Networks with Unsaturating Piecewise Linear Transfer Functions. Neural Comput. 15(3), 639–662 (2003)zbMATHCrossRefGoogle Scholar
  6. 6.
    Yi, Z., Tan, K.K.: Multistability of Discrete-Time Recurrent Neural Networks with Unsaturating Piecewise Linear Transfer Functions. IEEE Trans. Neural Networks 15(2), 329–336 (2004)CrossRefGoogle Scholar
  7. 7.
    Tan, K.C., Tang, H.J., Zhang, W.N.: Qualitative Analysis ror Recurrent Neural Networks with Linear Threshold Transfer Functions. IEEE Trans. Circuits Syst. I 52(5), 1003–1012 (2005)CrossRefMathSciNetGoogle Scholar
  8. 8.
    Wei, J.J., Ruan, S.G.: Stability and Bifurcation in a Neural Network Model with Two Delays. Physica D 130(3-4), 255–272 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Huang, L.H., Wu, J.: The Role of Threshold in Preventing Delay-Induced Oscillations of Frustrated Neural Networks with McCulloch-Pitts Nonlineearity. Game Theory and Algevra 11(6), 71–100 (2001)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Gopalsamy, K., Leung, I.: Delay Induced Periodicity in a Neural Network of Excitation an Inhibition. Physica D 89(3-4), 395–426 (1996)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hong Qu
    • 1
  • Zhang Yi
    • 1
  1. 1.Computational Intelligence Laboratory, School of Computer Science and EngineeringUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China

Personalised recommendations