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

TL;DR

This paper investigates how different transfer functions in a perceptron influence the long-term behavior of generated time series, revealing that non-monotonic functions can produce robust chaos and high-dimensional attractors.

Contribution

It provides a detailed analysis of the parameter space for various transfer functions, highlighting the conditions under which robust chaos and high-dimensional dynamics occur.

Findings

Non-monotonic transfer functions can generate robust chaos.

Monotonic functions produce fragile chaos.

High-dimensional chaotic attractors are linked to non-monotonic 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.