{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:02:44Z","timestamp":1760148164193,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,6]],"date-time":"2023-04-06T00:00:00Z","timestamp":1680739200000},"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":["AP09258737","N 120C138"],"award-info":[{"award-number":["AP09258737","N 120C138"]}]},{"name":"2247-A National Leading Researchers Program of TUBITAK, Turkey","award":["AP09258737","N 120C138"],"award-info":[{"award-number":["AP09258737","N 120C138"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A new model of inertial neural networks with a generalized piecewise constant argument as well as unpredictable inputs is proposed. The model is inspired by unpredictable perturbations, which allow to study the distribution of chaotic signals in neural networks. The existence and exponential stability of unique unpredictable and Poisson stable motions of the neural networks are proved. Due to the generalized piecewise constant argument, solutions are continuous functions with discontinuous derivatives, and, accordingly, Poisson stability and unpredictability are studied by considering the characteristics of continuity intervals. That is, the piecewise constant argument requires a specific component, the Poisson triple. The B-topology is used for the analysis of Poisson stability for the discontinuous functions. The results are demonstrated by examples and simulations.<\/jats:p>","DOI":"10.3390\/e25040620","type":"journal-article","created":{"date-parts":[[2023,4,6]],"date-time":"2023-04-06T03:59:55Z","timestamp":1680753595000},"page":"620","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Unpredictable and Poisson Stable Oscillations of Inertial Neural Networks with Generalized Piecewise Constant Argument"],"prefix":"10.3390","volume":"25","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":[{"role":"author","vocabulary":"crossref"}]},{"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, Almaty 050000, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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, Almaty 050000, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"112096","DOI":"10.1016\/j.chaos.2022.112096","article-title":"Spreading speeds of cellular neural networks model with time delay","volume":"160","author":"Bai","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.jmaa.2005.09.092","article-title":"Periodic bidirectional associative memory neural networks with distributed delays","volume":"317","author":"Chen","year":"2006","journal-title":"J. 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