Fuzzy operators and cyclic behavior in formal neuronal networks

Formal neuronal networks (FNN), which are comprised of threshold gates, make use of the unit step function. It is regarded as a degenerated distribution function (DDF) and will be referred to here as a non-fuzzy threshold operator (nFTO). Special networks of this kind generating long cycles of states are modified by introduction of fuzzy threshold operators (FTO), i.e., non-degenerated distribution functions (nDDF). The cyclic behavior of the new nets is compared with the original ones. The interconnection matrix and threshold values are not modified. It is concluded that the original long cycles change the fixed points and short cycles, and as the computer simulations demonstrate, the aperiodic motion that is associated with chaotic behavior appears. The emergence of the above changes depend on the steepness of the threshold operators.