Stability of quasi-periodic orbit in Discrete Recurrent Neural Network

  1. R. L. Marichal 1
  2. J. D. Piñeiro 1
  3. L. Moreno 1
  4. E. J. González 1
  5. J. Sigut 1
  6. S. Alayón 1
  1. 1 Universidad de La Laguna

    Universidad de La Laguna

    San Cristobal de La Laguna, España


WSEAS International Conference on Dynamical Systems and Control (1st.2005.Venice)

Publisher: World Scientific and Engineering Academy and Society (WSEAS)

ISBN: 960-8457-37-8

Year of publication: 2005

Pages: 586-591

Type: Conference paper


A simple discrete recurrent neural network model is considered. The local stability is analyzed withthe associated characteristic model. In order to study the quasi-periodic orbit dynamic behavior, it is necessary todeterminate the Neimark-Sacker bifurcation. In the case of two neurons, one necessary condition that producesthe Neimark-Sacker bifurcation is found. In addition to this, the stability and direction of the Neimark-Sacker aredetermined by applying the normal form theory and the center manifold theorem. An example is given andnumerical simulation are performed to illustrate the obtained results. The phase-locking is analyzed given someexperimental result of Arnold Tongue in determinate weight configuration.

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