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Stability of Quasi-Periodic Orbits in Recurrent Neural Networks

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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.

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Authors and Affiliations

  1. Department of Systems Engineering and Control and Computer Architecture, University of La Laguna, Avda. Francisco Sánchez S/N, Edf. Informatica, 38208, Tenerife, Canary Islands, Spain

    R. L. Marichal, J. D. Piñeiro, E. J. González & J. Torres

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  1. R. L. Marichal
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  2. J. D. Piñeiro
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  3. E. J. González
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  4. J. Torres
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Correspondence to R. L. Marichal.

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Marichal, R.L., Piñeiro, J.D., González, E.J. et al. Stability of Quasi-Periodic Orbits in Recurrent Neural Networks. Neural Process Lett 31, 269–281 (2010). https://doi.org/10.1007/s11063-010-9138-9

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