A directed-edge-reinforced random walk on graphs is considered. Criteria for the walk to end up in a limit cycle are given. Asymptotic stability of some neural networks is shown.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-3-4,
author = {J\'ozef Myjak and Ryszard Rudnicki},
title = {Reinforced walk on graphs and neural networks},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {255-268},
zbl = {1154.60360},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-3-4}
}
Józef Myjak; Ryszard Rudnicki. Reinforced walk on graphs and neural networks. Studia Mathematica, Tome 187 (2008) pp. 255-268. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm189-3-4/