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

We study the effect of various transfer functions on the properties of a time series generated by a continuous-valued feed-forward network in which the next input vector is determined from past output values. The parameter space for monotonic and nonmonotonic transfer functions is analyzed in the unstable regions with the following main finding: nonmonotonic functions can produce robust chaos whereas monotonic functions generate fragile chaos only. In the case of nonmonotonic functions, the number of positive Lyapunov exponents increases as a function of one of the free parameters in the model; hence, high dimensional chaotic attractors can be generated. We extend the analysis to a combination of monotonic and nonmonotonic functions.