Global bifurcations in a dynamical model of recurrent neural networks

Anita Windisch; Péter L. Simon

Applications of Mathematics (2023)

  • Volume: 68, Issue: 1, page 35-50
  • ISSN: 0862-7940

Abstract

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The dynamical behaviour of a continuous time recurrent neural network model with a special weight matrix is studied. The network contains several identical excitatory neurons and a single inhibitory one. This special construction enables us to reduce the dimension of the system and then fully characterize the local and global codimension-one bifurcations. It is shown that besides saddle-node and Andronov-Hopf bifurcations, homoclinic and cycle fold bifurcations may occur. These bifurcation curves divide the plane of weight parameters into nine domains. The phase portraits belonging to these domains are also characterized.

How to cite

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Windisch, Anita, and Simon, Péter L.. "Global bifurcations in a dynamical model of recurrent neural networks." Applications of Mathematics 68.1 (2023): 35-50. <http://eudml.org/doc/299353>.

@article{Windisch2023,
abstract = {The dynamical behaviour of a continuous time recurrent neural network model with a special weight matrix is studied. The network contains several identical excitatory neurons and a single inhibitory one. This special construction enables us to reduce the dimension of the system and then fully characterize the local and global codimension-one bifurcations. It is shown that besides saddle-node and Andronov-Hopf bifurcations, homoclinic and cycle fold bifurcations may occur. These bifurcation curves divide the plane of weight parameters into nine domains. The phase portraits belonging to these domains are also characterized.},
author = {Windisch, Anita, Simon, Péter L.},
journal = {Applications of Mathematics},
keywords = {saddle-node; Hopf; homoclinic; cycle fold bifurcation; Hopfield model},
language = {eng},
number = {1},
pages = {35-50},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global bifurcations in a dynamical model of recurrent neural networks},
url = {http://eudml.org/doc/299353},
volume = {68},
year = {2023},
}

TY - JOUR
AU - Windisch, Anita
AU - Simon, Péter L.
TI - Global bifurcations in a dynamical model of recurrent neural networks
JO - Applications of Mathematics
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 1
SP - 35
EP - 50
AB - The dynamical behaviour of a continuous time recurrent neural network model with a special weight matrix is studied. The network contains several identical excitatory neurons and a single inhibitory one. This special construction enables us to reduce the dimension of the system and then fully characterize the local and global codimension-one bifurcations. It is shown that besides saddle-node and Andronov-Hopf bifurcations, homoclinic and cycle fold bifurcations may occur. These bifurcation curves divide the plane of weight parameters into nine domains. The phase portraits belonging to these domains are also characterized.
LA - eng
KW - saddle-node; Hopf; homoclinic; cycle fold bifurcation; Hopfield model
UR - http://eudml.org/doc/299353
ER -

References

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