Cycle-symmetric matrices and convergent neural networks

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This work investigates a class of neural networks with cycle-symmetric connection strength. We shall show that, by changing the coordinates, the convergence of dynamics by Fiedler and Gedeon is equivalent to the classical results. This presentation also addresses the extension of the convergence theorem to other classes of signal functions with saturations. In particular, the result of Cohen and Grossberg is recast and extended with a more concise verification.

Original languageEnglish
Pages (from-to)213-220
Number of pages8
JournalPhysica D: Nonlinear Phenomena
Issue number1-4
StatePublished - 15 Nov 2000


  • Neural networks
  • Cycle-symmetric matrix
  • Lyapunov function
  • Convergence of dynamics


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