Stability of Quasi-Periodic Orbits in Recurrent Neural Networks

Authors:
R. L. Marichal;J. D. Piñeiro;E. J. González;J. Torres
Affiliations:
Department of Systems Engineering and Control and Computer Architecture, University of La Laguna, Tenerife, Spain 38208;Department of Systems Engineering and Control and Computer Architecture, University of La Laguna, Tenerife, Spain 38208;Department of Systems Engineering and Control and Computer Architecture, University of La Laguna, Tenerife, Spain 38208;Department of Systems Engineering and Control and Computer Architecture, University of La Laguna, Tenerife, Spain 38208
Venue:
Neural Processing Letters
Year:
2010

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Abstract

A simple discrete recurrent neural network model is considered. The local stability is analyzed with the associated characteristic model. In order to study the dynamic behavior of the quasi-periodic orbit, it is necessary to determine the Neimark-Sacker bifurcation. In the case of two neurons, one necessary condition that yields the Neimark-Sacker bifurcation is found. In addition to this, the stability and direction of the Neimark-Sacker bifurcation are determined by applying normal form theory and the center manifold theorem. An example is given and a numerical simulation is performed to illustrate the results. The phase-locking phenomena are analyzed for certain experimental results with Arnold Tongues in a particular weight configuration.