TR: Embedding Recurrent Neural Networks into Predator-Prey Models

[Yves Moreau]

Dear Connectionists,

The following technical report is available via ftp or the World Wide
Web:


EMBEDDING RECURRENT NEURAL NETWORKS INTO PREDATOR-PREY MODELS

Yves Moreau and Joos Vandewalle, K.U.Leuven ESAT-SISTA

K.U.Leuven, Elektrotechniek-ESAT, Technical report ESAT-SISTA TR98-02
ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/moreau/reports/lotka_volterra_tr98-02.ps

Comments are more than welcome!

ABSTRACT
========

  We study changes of coordinates that allow the embedding of the
  ordinary differential equations describing continuous-time recurrent
  neural networks into differential equations describing predator-prey
models
  ---also called Lotka-Volterra systems. We do this by transforming
  the equations for the neural network first into quasi-monomial form,
  where we express the vector field of the dynamical
  system as a linear combination of products of powers of the
  variables.  From this quasi-monomial form, we can directly
  transform the system further into Lotka-Volterra equations.  The
  resulting Lotka-Volterra system is of higher dimension than the
  original system, but the behavior of its first variables is
  equivalent to the behavior of the original neural network. We expect
  that this transformation will permit the application of existing
techniques
  for the analysis of Lotka-Volterra systems to recurrent-neural
  networks. Furthermore, our result shows that Lotka-Volterra systems
are
  universal approximators of dynamical systems, just as
  continuous-time neural networks.

Keywords: Continuous-time neural networks,
Equivalence of dynamical systems, Lotka-Volterra systems,
Predator-prey models, Quasi-monomial forms.

--------------------------------------------------------------

To get it from the World Wide Web, point your browser at:
ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/moreau/reports/lotka_volterra_tr98-02.ps

To get it via FTP:
ftp ftp.esat.kuleuven.ac.be
cd pub/SISTA/moreau/reports
get lotka_volterra_tr98-02.ps


--------------------

Yves Moreau

Department of Electrical Engineering
Katholieke Universiteit Leuven
Leuven, Belgium

email: moreau at esat.kuleuven.ac.be

homepage: http://www.esat.kuleuven.ac.be/~moreau

publications:
http://www.esat.kuleuven.ac.be/~moreau/publication_list.html