Input space bifurcation manifolds of recurrent neural networks

Authors:
Robert Haschke;Jochen J. Steil
Affiliations:
Bielefeld University, Neuroinformatics Group, Faculty of Technology, P. O. Box 10 01 31, D-33501 Bielefeld, Germany;Bielefeld University, Neuroinformatics Group, Faculty of Technology, P. O. Box 10 01 31, D-33501 Bielefeld, Germany
Venue:
Neurocomputing
Year:
2005

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Abstract

We derive analytical expressions of local codimension-1 bifurcations for a fully connected, additive, discrete-time recurrent neural network (RNN), where we regard the external inputs as bifurcation parameters. The complexity of the bifurcation diagrams obtained increases exponentially with the number of neurons. We show that a three-neuron cascaded network can serve as a universal oscillator, whose amplitude and frequency can be completely controlled by input parameters.