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Comparison on Gradient-Based Neural Dynamics and Zhang Neural Dynamics for Online Solution of Nonlinear Equations

  • Yunong Zhang
  • Chenfu Yi
  • Weimu Ma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5370)

Abstract

For online solution of nonlinear equation f(x) = 0, this paper generalizes a special kind of recurrent neural dynamics by using a recent design method proposed by Zhang et al. Different from gradient-based dynamics (GD), the resultant Zhang dynamics (ZD) is designed based on the elimination of an indefinite error-monitoring function (instead of the elimination of a square-based positive error-function usually associated with GD). For comparative purposes, the gradient-based dynamics is also developed and exploited for solving online such a nonlinear equation f(x) = 0. Computer-simulation results via power-sigmoid activation functions substantiate further the theoretical analysis and efficacy of Zhang neural dynamics on nonlinear equations solving.

Keywords

Recurrent neural networks neural dynamics nonlinear equations activation functions exponential convergence 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Yunong Zhang
    • 1
  • Chenfu Yi
    • 1
  • Weimu Ma
    • 1
  1. 1.School of Information Science and TechnologySun Yat-Sen UniversityGuangzhouChina

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