Long-term properties of time series generated by a perceptron with varioustransfer functions

We study the effect of various transfer functions on the properties of a ti me series generated by a continuous-valued feed-forward network in which th e next input vector is determined from past output values. The parameter sp ace for monotonic and nonmonotonic transfer functions is analyzed in the un stable regions with the following main finding: nonmonotonic functions can produce robust chaos whereas monotonic functions generate fragile chaos onl y. In the case of nonmonotonic functions, the number of positive Lyapunov e xponents increases as a function of one of the free parameters in the model ; hence, high dimensional chaotic attractors can be generated. We extend th e analysis to a combination of monotonic and nonmonotonic functions. [S1063 -651X(99)02303-X].