{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T22:24:19Z","timestamp":1775687059060,"version":"3.50.1"},"reference-count":40,"publisher":"World Scientific Pub Co Pte Ltd","issue":"08","funder":[{"name":"Hubei International Science and Technology Cooperation Base of Fish Passage","award":["HIBF2020006"],"award-info":[{"award-number":["HIBF2020006"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12026233"],"award-info":[{"award-number":["12026233"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12026221"],"award-info":[{"award-number":["12026221"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61966039"],"award-info":[{"award-number":["61966039"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2021,6,30]]},"abstract":"<jats:p> We propose a nonsmooth Filippov refuge ecosystem with a piecewise saturating response function and analyze its dynamics. We first investigate some key elements to our model which include the sliding segment, the sliding mode dynamics and the existence of equilibria which are classified into regular\/virtual equilibrium, pseudo-equilibrium, boundary equilibrium and tangent point. In particular, we consider how the existence of the regular equilibrium and the pseudo-equilibrium are related. Then we study the stability of the standard periodic solution (limit cycle), the sliding periodic solutions (grazing or touching cycle) and the dynamics of the pseudo equilibrium, using quantitative analysis techniques related to nonsmooth Filippov systems. Furthermore, as the threshold value is varied, the model exhibits several complex bifurcations which are classified into equilibria, sliding mode, local sliding (boundary node and focus) and global bifurcations (grazing or touching). In conclusion, we discuss the importance of the refuge strategy in a biological setting. <\/jats:p>","DOI":"10.1142\/s0218127421501194","type":"journal-article","created":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T08:18:33Z","timestamp":1624868313000},"page":"2150119","source":"Crossref","is-referenced-by-count":8,"title":["Sliding Dynamics and Bifurcations in the Extended Nonsmooth Filippov Ecosystem"],"prefix":"10.1142","volume":"31","author":[{"given":"Wenjie","family":"Qin","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, P. R. China"},{"name":"Hubei International Science and Technology Cooperation Base of Fish Passage, China Three Gorges University, Yichang 443002, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4710-2325","authenticated-orcid":false,"given":"Xuewen","family":"Tan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650500, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaotao","family":"Shi","sequence":"additional","affiliation":[{"name":"Hubei International Science and Technology Cooperation Base of Fish Passage, China Three Gorges University, Yichang 443002, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marco","family":"Tosato","sequence":"additional","affiliation":[{"name":"Laboratory for Industrial and Applied Mathematics, York University, Toronto M3J 1P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinzhi","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Waterloo, Waterloo N2L 3G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,6,26]]},"reference":[{"key":"S0218127421501194BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-7824(03)00071-0"},{"key":"S0218127421501194BIB002","doi-asserted-by":"publisher","DOI":"10.1137\/17M1110328"},{"key":"S0218127421501194BIB003","doi-asserted-by":"publisher","DOI":"10.1137\/050627757"},{"key":"S0218127421501194BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2006.08.017"},{"key":"S0218127421501194BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s10883-013-9169-4"},{"key":"S0218127421501194BIB006","volume-title":"Controlling Chaos and Bifurcations in Engineering Systems","author":"Chen G.","year":"1999"},{"key":"S0218127421501194BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/0092-8240(94)00024-7"},{"key":"S0218127421501194BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02124750"},{"key":"S0218127421501194BIB009","doi-asserted-by":"publisher","DOI":"10.1137\/050625060"},{"key":"S0218127421501194BIB010","doi-asserted-by":"publisher","DOI":"10.1137\/080724599"},{"key":"S0218127421501194BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2014.03.024"},{"key":"S0218127421501194BIB012","first-page":"265","author":"Filippov A. F.","year":"1988","journal-title":"Nonlin. Anal. Nonlin. Diff. Eqs."},{"key":"S0218127421501194BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/S0092-8240(86)90004-2"},{"key":"S0218127421501194BIB014","doi-asserted-by":"publisher","DOI":"10.1126\/science.79.2036.16-a"},{"key":"S0218127421501194BIB015","doi-asserted-by":"publisher","DOI":"10.2307\/1087"},{"key":"S0218127421501194BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2010.11.016"},{"key":"S0218127421501194BIB017","doi-asserted-by":"publisher","DOI":"10.1134\/S1560354712030069"},{"key":"S0218127421501194BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2011.01.016"},{"key":"S0218127421501194BIB019","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403007874"},{"key":"S0218127421501194BIB020","doi-asserted-by":"publisher","DOI":"10.1137\/080722886"},{"key":"S0218127421501194BIB021","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1995.0346"},{"key":"S0218127421501194BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2014.09.014"},{"key":"S0218127421501194BIB023","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2016.02.042"},{"key":"S0218127421501194BIB024","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127419500202"},{"key":"S0218127421501194BIB025","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2019.06.046"},{"key":"S0218127421501194BIB026","doi-asserted-by":"publisher","DOI":"10.1086\/284865"},{"key":"S0218127421501194BIB027","first-page":"864","volume":"5","author":"Slebodzinski W.","year":"1931","journal-title":"Bull. de l\u2019Academie royale de Belgique"},{"key":"S0218127421501194BIB028","doi-asserted-by":"publisher","DOI":"10.1137\/110847020"},{"key":"S0218127421501194BIB029","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2012.08.013"},{"key":"S0218127421501194BIB030","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127414501223"},{"key":"S0218127421501194BIB031","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1977.1101446"},{"key":"S0218127421501194BIB032","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-84379-2_1"},{"key":"S0218127421501194BIB033","doi-asserted-by":"publisher","DOI":"10.1201\/9781420065619"},{"key":"S0218127421501194BIB034","doi-asserted-by":"publisher","DOI":"10.1137\/0720098"},{"key":"S0218127421501194BIB035","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-018-1313-z"},{"key":"S0218127421501194BIB036","doi-asserted-by":"publisher","DOI":"10.1142\/S021812740100336X"},{"key":"S0218127421501194BIB037","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-012-9758-5"},{"key":"S0218127421501194BIB038","doi-asserted-by":"publisher","DOI":"10.3934\/mbe.2013.10.445"},{"key":"S0218127421501194BIB039","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2018.2836386"},{"key":"S0218127421501194BIB040","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2012.09.005"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127421501194","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,28]],"date-time":"2021-06-28T08:20:15Z","timestamp":1624868415000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127421501194"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,26]]},"references-count":40,"journal-issue":{"issue":"08","published-print":{"date-parts":[[2021,6,30]]}},"alternative-id":["10.1142\/S0218127421501194"],"URL":"https:\/\/doi.org\/10.1142\/s0218127421501194","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,26]]}}}