Noisy time series generation by feed-forward networks

DOI10.1088/0305-4470/31/4/009zbMATH Open0903.68163arXivcond-mat/9803267OpenAlexW1978749140MaRDI QIDQ3839319

Author name not available (Why is that?)

Publication date: 3 November 1998

Published in: (Search for Journal in Brave)

Abstract: We study the properties of a noisy time series generated by a continuous-valued feed-forward network in which the next input vector is determined from past output values. Numerical simulations of a perceptron-type network exhibit the expected broadening of the noise-free attractor, without changing the attractor dimension. We show that the broadening of the attractor due to the noise scales inversely with the size of the system ,$N$, as $1/sqrtN$. We show both analytically and numerically that the diffusion constant for the phase along the attractor scales inversely with $N$. Hence, phase coherence holds up to a time that scales linearly with the size of the system. We find that the mean first passage time, $t$, to switch between attractors depends on $N$, and the reduced distance from bifurcation $au$ as $t=aNoverauexp(bau{N}^{1/2})$, where $b$ is a constant which depends on the amplitude of the external noise. This result is obtained analytically for small $au$ and confirmed by numerical simulations.

Full work available at URL: https://arxiv.org/abs/cond-mat/9803267

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Noisy time series generation by feed-forward networks

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q3839319)