{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T20:55:54Z","timestamp":1782593754478,"version":"3.54.5"},"reference-count":29,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,9,22]],"date-time":"2023-09-22T00:00:00Z","timestamp":1695340800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan","award":["AP14870835"],"award-info":[{"award-number":["AP14870835"]}]},{"name":"Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan","award":["120C138"],"award-info":[{"award-number":["120C138"]}]},{"name":"National Leading Researchers Program of TUBITAK, Turkey","award":["AP14870835"],"award-info":[{"award-number":["AP14870835"]}]},{"name":"National Leading Researchers Program of TUBITAK, Turkey","award":["120C138"],"award-info":[{"award-number":["120C138"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper explores the novel concept of discontinuous unpredictable and Poisson-stable motions within impulsive inertial neural networks. The primary focus is on a specific neural network architecture where impulses mimic the structure of the original model, that is, continuous and discrete parts are symmetrical. This unique modeling decision aligns with the real-world behavior of systems, where voltage typically remains smooth and continuous but may exhibit sudden changes due to various factors such as switches, sudden loads, or faults. The paper introduces the representation of these abrupt voltage transitions as discontinuous derivatives, providing a more accurate depiction of real-world scenarios. Thus, the focus of the research is a model, exceptional in its generality. To study Poisson stability, the method of included intervals is extended for discontinuous functions and B-topology. The theoretical findings are substantiated with numerical examples, demonstrating the practical feasibility of the proposed model.<\/jats:p>","DOI":"10.3390\/sym15101812","type":"journal-article","created":{"date-parts":[[2023,9,24]],"date-time":"2023-09-24T10:40:22Z","timestamp":1695552022000},"page":"1812","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Symmetrical Impulsive Inertial Neural Networks with Unpredictable and Poisson-Stable Oscillations"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2985-286X","authenticated-orcid":false,"given":"Marat","family":"Akhmet","sequence":"first","affiliation":[{"name":"Department of Mathematics, Middle East Technical University, Ankara 06800, Turkey"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5572-2305","authenticated-orcid":false,"given":"Madina","family":"Tleubergenova","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aktobe Regional University, Aktobe 030000, Kazakhstan"},{"name":"Institute of Information and Computational Technologies CS MES RK, Almaty 050000, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Roza","family":"Seilova","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aktobe Regional University, Aktobe 030000, Kazakhstan"},{"name":"Institute of Information and Computational Technologies CS MES RK, Almaty 050000, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3206-3877","authenticated-orcid":false,"given":"Zakhira","family":"Nugayeva","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Aktobe Regional University, Aktobe 030000, Kazakhstan"},{"name":"Institute of Information and Computational Technologies CS MES RK, Almaty 050000, Kazakhstan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"11555","DOI":"10.1007\/s00521-021-05833-x","article-title":"Sliding mode control based fixed-time stabilization and synchronization of inertial neural networks with time-varying delays","volume":"33","author":"Aouiti","year":"2021","journal-title":"Neural Comput. 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