Fractal encoding in a chaotic neural network.

We analyze a model of a chaotic neural network consisting of three neurons, namely a chaotically forcing neuron and two neurons comprizing a stable response system with a contraction mapping property, for digital encoding with chaotic dynamics. We show that dynamics of the chaotically forcing neuron is embedded in the form of a code sequence on a fractal attractor of the two-neuron response system. We consider the relation between the state transition of the chaotically forcing neuron and the hierarchical fractal structure on the attractor in the state space of the contracting system. We also report hardware implementation of the presented model with an analog electronic circuit to investigate the fractal attractor of the chaotic neural network as a realistic system.