paper on time series generation

[Avner Priel]

The following paper on the subject of time series generation by
feed-forward networks has appeared on the 
Journal of Physics A 31(4) 1189 (1998).

The paper is available from my home-page :

	http://faculty.biu.ac.il/~priel/

comments are welcome.


*************** NO HARD COPIES ******************


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Noisy time series generation by feed-forward networks
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A Priel, I Kanter and D A Kessler

Department of Physics, Bar Ilan University, 52900 Ramat Gan,Israel


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 $1/ \sqrt{N}$.
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 $\tau$ as $t = a {N \over \tau} \exp(b \tau N^{1/2})$, 
where $b$ is a constant which depends on the 
amplitude of the external noise. This result is obtained analytically 
for small $\tau$ and confirmed by numerical simulations.



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  Priel Avner  < priel at mail.biu.ac.il >           
  	       < http://faculty.biu.ac.il/~priel >
  Department of Physics,  Bar-Ilan University.            
  Ramat-Gan, 52900.             
  Israel.