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

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

1998-11-08

arxiv.org/abs/cond-mat/9811109v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 two-columns Latex pages including 8 figures. Submitted to Physical Review E. For full quality figures, see http://faculty.bi

Scientific paper

10.1103/PhysRevE.59.3368

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.

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