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/