Input Space Bifurcation Manifolds of RNNs

We derive analytical expressions of local codim-1-bifurcations for a fully connected, additive, discrete-time 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.

• Type: Conference
• Year: 2004
• Where: ESANN
• Authors: Robert Haschke, Jochen J. Steil
• Keywords: Bifurcation Parameters, Diagrams Obtained Increases, ESANN 2004, ESANN 2007, Three-neuron Cascaded Network