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

Abstract

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 non-monotonic transfer functions is analyzed in the unstable regions with the following main finding; non-monotonic functions can produce robust chaos whereas monotonic functions generate fragile chaos only. In the case of non-monotonic 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 non-monotonic functions.