Convergence analysis of continuous-time neural networks

  • Authors:

  • Min-Jae Kang;Ho-Chan Kim;Farrukh A. Khan;Wang-Cheol Song;Jacek M. Zurada

  • Affiliations:

  • Faculty of Electrical & Electronic Engineering, Cheju National University, Jeju, South Korea;Faculty of Electrical & Electronic Engineering, Cheju National University, Jeju, South Korea;Department of Computer Engineering, Cheju National University, Jeju, South Korea;Department of Computer Engineering, Cheju National University, Jeju, South Korea;Department of Electrical Engineering, University of Louisville, Louisville, KY

  • Venue:
  • ISNN'06 Proceedings of the Third international conference on Advances in Neural Networks - Volume Part I
  • Year:
  • 2006

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Abstract

The energy function of continuous-time neural network has been analyzed for testing the existence of stationary points and the global convergence of network. The energy function always has only one stationary point which is a saddle point in the unconstrained space when the total conductance of neuron’s input is zero (Gi = 0). However, the stationary points exist only inside the hypercube Rn ∈[0,1] when the total conductance of neuron’s input is not zero (Gi ≠ 0). The Hessian matrix of the energy function is used for testing the global convergence of the network.