{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T14:05:56Z","timestamp":1776521156951,"version":"3.51.2"},"reference-count":34,"publisher":"IOP Publishing","issue":"4","license":[{"start":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T00:00:00Z","timestamp":1582848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/publishingsupport.iopscience.iop.org\/iop-standard\/v1"},{"start":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T00:00:00Z","timestamp":1582848000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","award":["UID\/MAT\/00144\/2019"],"award-info":[{"award-number":["UID\/MAT\/00144\/2019"]}]},{"name":"FEDER \u2014 NORTE 2020 \u2014 Portugal","award":["STRIDE [NORTE-01-0145- FEDER-000033]"],"award-info":[{"award-number":["STRIDE [NORTE-01-0145- FEDER-000033]"]}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Nonlinearity"],"published-print":{"date-parts":[[2020,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We provide conditions guaranteeing that certain classes of robust heteroclinic networks are asymptotically stable.<\/jats:p>\n                  <jats:p>\n                    We study the asymptotic stability of ac-networks\u2014robust heteroclinic networks that exist in smooth\n                    <jats:inline-formula\/>\n                    -equivariant dynamical systems defined in the positive orthant of\n                    <jats:inline-formula\/>\n                    . Generators of the group\n                    <jats:inline-formula\/>\n                    are the transformations that change the sign of one of the spatial coordinates. The ac-network is a union of hyperbolic equilibria and connecting trajectories, where all equilibria belong to the coordinate axes (not more than one equilibrium per axis) with unstable manifolds of dimension one or two. The classification of ac-networks is carried out by describing all possible types of associated graphs.\n                  <\/jats:p>\n                  <jats:p>We prove sufficient conditions for asymptotic stability of ac-networks. The proof is given as a series of theorems and lemmas that are applicable to the ac-networks and to more general types of networks. Finally, we apply these results to discuss the asymptotic stability of several examples of heteroclinic networks.<\/jats:p>","DOI":"10.1088\/1361-6544\/ab6817","type":"journal-article","created":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T11:13:36Z","timestamp":1582888416000},"page":"1757-1788","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":11,"title":["Asymptotic stability of robust heteroclinic networks"],"prefix":"10.1088","volume":"33","author":[{"given":"Olga","family":"Podvigina","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9029-6893","authenticated-orcid":false,"given":"Sofia B S D","family":"Castro","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1131-8746","authenticated-orcid":false,"given":"Isabel S","family":"Labouriau","sequence":"additional","affiliation":[]}],"member":"266","published-online":{"date-parts":[[2020,2,28]]},"reference":[{"key":"nonab6817bib001","doi-asserted-by":"publisher","first-page":"1645","DOI":"10.1088\/0951-7715\/29\/5\/1645","type":"journal-article","article-title":"Two-dimensional heteroclinic attractor in the generalized Lotka\u2013Volterra system","volume":"29","author":"Afraimovich","year":"2016","journal-title":"Nonlinearity"},{"key":"nonab6817bib002","author":"Anosov","year":"1988","type":"book"},{"key":"nonab6817bib003","doi-asserted-by":"publisher","article-title":"Almost complete and equable heteroclinic networks","author":"Ashwin","DOI":"10.1007\/s00332-019-09566-z)","type":"web-resource"},{"key":"nonab6817bib004","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.physd.2013.09.006","type":"journal-article","article-title":"On designing heteroclinic networks from graphs","volume":"265","author":"Ashwin","year":"2013","journal-title":"Physica D"},{"key":"nonab6817bib005","doi-asserted-by":"publisher","first-page":"1367","DOI":"10.1088\/0951-7715\/7\/5\/006","type":"journal-article","article-title":"Heteroclinic networks on the tetrahedron","volume":"7","author":"Brannath","year":"1994","journal-title":"Nonlinearity"},{"key":"nonab6817bib006","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1126\/science.208.4440.173","type":"journal-article","article-title":"Convection in a rotating layer: a simple case of turbulence","volume":"208","author":"Busse","year":"1980","journal-title":"Science"},{"key":"nonab6817bib007","doi-asserted-by":"publisher","first-page":"3677","DOI":"10.1088\/0951-7715\/29\/12\/3677","type":"journal-article","article-title":"Construction of heteroclinic networks in R4","volume":"29","author":"Castro","year":"2016","journal-title":"Nonlinearity"},{"key":"nonab6817bib008","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physd.2018.01.008","type":"journal-article","article-title":"Pseudo-simple heteroclinic cycles in R4","volume":"372","author":"Chossat","year":"2018","journal-title":"Physica D"},{"key":"nonab6817bib009","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1007\/BF02683825","type":"journal-article","article-title":"The heteroclinic cycle in the model of competition between n species and its stability","volume":"14","author":"Feng","year":"1998","journal-title":"Acta Math. 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All rights, including for text and data mining, AI training, and similar technologies, are reserved.","name":"copyright_information","label":"Copyright Information"},{"value":"2019-05-15","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2020-01-06","name":"date_accepted","label":"Date Accepted","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"2020-02-28","name":"date_epub","label":"Online publication date","group":{"name":"publication_dates","label":"Publication dates"}}]}}