Chaotic neuron models and artificial neural networks

We review models of chaotic neurons for information processing. Besides differential flows, two discrete maps are motivated by a giant squid axon measurement but differ in the delay strategy for generating chaos: (i) 2-D He´non-like discrete maps which are equivalent to 1-D maps with integer delays for replenishments; (ii) 1-D Feigenbaum-like one-step discrete maps, e.g. NL σ_N neurons producing chaos via the bifurcation cascades. ANN of σ_N generates chaos due to the change of mean fields of feedback baseline slopes, i.e. different from Aihara circuits and Yamakawa chips of single element. ANN having 10⁵ chaotic neurons dynamics showed useful fuzzy logic reasoning via neural images by Szu et al. Smaller networks are studied in this paper to investigate the transition to chaos in the Hebbian learning networks of σ_N neurons. Different sizes of ANN are studied ranging from 2 to 25 neurons. Chaotic I/O mapping was found in each with a gradually narrowing window.