{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:52:59Z","timestamp":1753876379581,"version":"3.41.2"},"reference-count":35,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T00:00:00Z","timestamp":1740096000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100006407","name":"Natural Science Foundation of Henan Province","doi-asserted-by":"publisher","award":["242300420247"],"award-info":[{"award-number":["242300420247"]}],"id":[{"id":"10.13039\/501100006407","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Universities of Henan Province","award":["NSFRF240815"],"award-info":[{"award-number":["NSFRF240815"]}]},{"name":"Program of Young Scholar for Henan Polytechnic University","award":["2020XQG-03"],"award-info":[{"award-number":["2020XQG-03"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,2,21]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This research aims to investigate the stochastic stabilization and destabilization of hybrid stochastic differential equations (SDEs) with L\u00e9vy noise. First, the sufficient conditions for stability and instability of hybrid SDEs systems with L\u00e9vy noise are given. Based on these, this paper is then devoted to the effects of the noise (Brownian motion noise and L\u00e9vy noise) on stability and instability of hybrid differential equation system. For the more comprehensive analysis, we establish the criteria for the stable and unstable behaviours of the general linear hybrid SDEs systems perturbed by L\u00e9vy noise. Last, we reveal a fact that only L\u00e9vy noise or Brownian motion noise and L\u00e9vy noise together cannot destabilize the stability of a 1D linear stable system, the similar effect occurred in Mao et\u00a0al. (2007), which states that only Brownian motion noise cannot destroy the stability of a 1D linear stable system.<\/jats:p>","DOI":"10.1093\/imamci\/dnaf007","type":"journal-article","created":{"date-parts":[[2025,5,7]],"date-time":"2025-05-07T17:45:16Z","timestamp":1746639916000},"source":"Crossref","is-referenced-by-count":0,"title":["Stochastic stabilization and destabilization of hybrid SDEs driven by L\u00e9vy noise"],"prefix":"10.1093","volume":"42","author":[{"given":"Guixin","family":"Hu","sequence":"first","affiliation":[{"name":"School of Mathematics and Information Science , Henan Polytechnic University, Jiaozuo 454003,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-3862-8055","authenticated-orcid":false,"given":"Zhihao","family":"Geng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Science , Henan Polytechnic University, Jiaozuo 454003,","place":["China"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,5,7]]},"reference":[{"key":"2025052712283989800_ref1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3038-0","volume-title":"Continuous-Time Markov Chains","author":"Anderson","year":"1991"},{"key":"2025052712283989800_ref2","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511809781","volume-title":"L\u00e9vy Processes and Stochastic Calculus","author":"Applebaum","year":"2009"},{"key":"2025052712283989800_ref3","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1142\/S0219493710003066","article-title":"Stochastic stabilization of dynamical systems using L\u00e9vy noise","volume":"10","author":"Applebaum","year":"2010","journal-title":"Stoch. 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