{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:57:02Z","timestamp":1760147822090,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,3]],"date-time":"2023-03-03T00:00:00Z","timestamp":1677801600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"NSFC","award":["12001213"],"award-info":[{"award-number":["12001213"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The Koper model is a vector field in which the differential equations describe the electrochemical oscillations appearing in diffusion processes. This work focuses on the understanding of the slow dynamics of a stochastic Koper model perturbed by stable L\u00e9vy noise. We establish the slow manifold for a stochastic Koper model with stable L\u00e9vy noise and verify exponential tracking properties. We also present two practical examples to demonstrate the analytical results with numerical simulations.<\/jats:p>","DOI":"10.3390\/axioms12030261","type":"journal-article","created":{"date-parts":[[2023,3,3]],"date-time":"2023-03-03T02:03:08Z","timestamp":1677808988000},"page":"261","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Slow Manifolds for Stochastic Koper Models with Stable L\u00e9vy Noises"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1903-381X","authenticated-orcid":false,"given":"Hina","family":"Zulfiqar","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Okara, Okara 56300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4427-7795","authenticated-orcid":false,"given":"Shenglan","family":"Yuan","sequence":"additional","affiliation":[{"name":"Institut f\u00fcr Mathematik, Universit\u00e4t Augsburg, 86135 Augsburg, Germany"},{"name":"Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Shoaib","family":"Saleem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Okara, Okara 56300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/0167-2789(95)90061-6","article-title":"Bifurcations of mixed-mode oscillations in a three-variable autonomous Van der Pol-Duffing model with a cross-shaped phase diagram","volume":"80","author":"Koper","year":"1995","journal-title":"Phys. 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