Microsoft Word - wseas-full.rtf

A simple discrete recurrent neural network model is considered. The local stability is analyzed with the associated characteristic model. In order to study the quasi-periodic orbit dynamic behavior, it is necessary to determinate the Neimark-Sacker bifurcation. In the case of two neurons, one necessary condition that produces the Neimark-Sacker bifurcation is found. In addition to this, the stability and direction of the Neimark-Sacker are determined by applying the normal form theory and the center manifold theorem. An example is given and numerical simulation are performed to illustrate the obtained results. The phase-locking is analyzed given some experimental result of Arnold Tongue in determinate weight configuration. Key-Words: Nonlinear System, Neural Networks, Bifurcation, Neimark Sacker, Arnold Tongue, Quasi-periodic orbit.