{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T15:55:15Z","timestamp":1784303715157,"version":"3.55.0"},"reference-count":50,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T00:00:00Z","timestamp":1772150400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong province","doi-asserted-by":"publisher","award":["ZR2022MG059"],"award-info":[{"award-number":["ZR2022MG059"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013139","name":"Humanities and Social Science Fund of Ministry of Education of China","doi-asserted-by":"publisher","award":["23YJAZH084"],"award-info":[{"award-number":["23YJAZH084"]}],"id":[{"id":"10.13039\/501100013139","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Graduate Excellent Course Construction Project of Shandong Province: Applied Statistics","award":["SDJKC2023010"],"award-info":[{"award-number":["SDJKC2023010"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a continuous-time dynamic clearing model on a multilayer financial network to study systemic risk propagation and optimal intervention. The model incorporates interbank credit, equity crossholdings, and overlapping portfolios, and models bankruptcy as a jump event triggered by insolvency or illiquidity. Based on the system\u2019s dynamic structure, we develop a model predictive control (MPC) framework that enables forward-looking and flexible allocation of limited bailout resources between debt relief and capital injection. Numerical results show that the proposed MPC strategy substantially outperforms both no-intervention and rule-based policies in terms of financial stability and resource efficiency. Compared with no intervention, the MPC strategy reduces the number of defaulting banks by approximately 56%. In contrast, the simple rule-based intervention achieves a reduction of about 48.83%, while improving rescue efficiency by approximately 28.57%. Overall, the framework provides a unified and effective approach to systemic risk control in financial networks.<\/jats:p>","DOI":"10.3390\/axioms15030166","type":"journal-article","created":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T15:52:38Z","timestamp":1772207558000},"page":"166","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Nonlinear Dynamic Model of Risk Propagation and Optimal Control Strategy in Multilayer Financial Networks"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5670-3846","authenticated-orcid":false,"given":"Yi","family":"Ding","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Yin","sequence":"additional","affiliation":[{"name":"Rizhao Municipal Bureau of Finance, Rizhao 276826, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chun","family":"Yan","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-3602-8296","authenticated-orcid":false,"given":"Yufei","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"065203","DOI":"10.1088\/1402-4896\/ad3bed","article-title":"Analytic solutions of alpha-beta-time-derivatives complex finance chaotic dynamical system: Synchronization and extended center manifold. 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