{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:06:58Z","timestamp":1753880818997,"version":"3.41.2"},"reference-count":22,"publisher":"World Scientific Pub Co Pte Ltd","issue":"16","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61807006"],"award-info":[{"award-number":["61807006"]}],"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":[[2022,12,30]]},"abstract":"<jats:p> In this paper, a delayed rumor propagation model with a discontinuous control mechanism is investigated. First, we investigate the model\u2019s existence and boundedness. Then, conditions for the existence of the rumor-endemic equilibrium are derived utilizing differential inclusions. We examine the local asymptotic stability and Hopf bifurcation of the rumor-endemic equilibrium when the discontinuous control function is differential at the rumor-endemic equilibrium, considering the delay as the bifurcating parameter. When the discontinuous control function is not differential at the rumor-endemic equilibrium, we investigate the global asymptotically stable rumor-free and rumor-endemic equilibria using the Lyapunov functional technique. We conclude by providing two examples to validate our theoretical predictions. It is demonstrated that delay is a critical system parameter that can result in both Hopf bifurcation and chaos. <\/jats:p>","DOI":"10.1142\/s021812742250242x","type":"journal-article","created":{"date-parts":[[2023,1,15]],"date-time":"2023-01-15T03:02:18Z","timestamp":1673751738000},"source":"Crossref","is-referenced-by-count":3,"title":["Stability and Hopf Bifurcation Analyses of a Delayed Rumor Spreading Model and Its Discontinuous Control"],"prefix":"10.1142","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3205-1051","authenticated-orcid":false,"given":"Honglan","family":"Zhu","sequence":"first","affiliation":[{"name":"Business School, Huaiyin Institute of Technology, Huai\u2019an 223003, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuebing","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. 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