{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,22]],"date-time":"2025-10-22T03:08:33Z","timestamp":1761102513586,"version":"build-2065373602"},"reference-count":51,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,8,23]],"date-time":"2022-08-23T00:00:00Z","timestamp":1661212800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Committee of then Ministry of Education and Science of the Republic of Kazakhstan","award":["AP09258737","AP08856170","120C138"],"award-info":[{"award-number":["AP09258737","AP08856170","120C138"]}]},{"name":"2247-A National Leading Researchers Program of TUBITAK, Turkey","award":["AP09258737","AP08856170","120C138"],"award-info":[{"award-number":["AP09258737","AP08856170","120C138"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the continuous time, but also the generalized piecewise constant argument. The process is subdued to Poisson stable inputs, which cause the new type of recurrent signals. The method of included intervals, recently introduced approach of recurrent motions checking, is effectively utilized. The existence and asymptotic properties of the unique Poisson stable motion are investigated. Simulation examples for results are provided. Finally, comparing impulsive shunting inhibitory cellular neural networks with former neural network models, we discuss the significance of the components of our model.<\/jats:p>","DOI":"10.3390\/sym14091754","type":"journal-article","created":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T02:55:34Z","timestamp":1661309734000},"page":"1754","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument"],"prefix":"10.3390","volume":"14","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, 06800 Ankara, 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 CS MES RK, Almaty 050010, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4666-8001","authenticated-orcid":false,"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 050010, 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 CS MES RK, Almaty 050010, Kazakhstan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,8,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1109\/31.7600","article-title":"Cellular neural networks: Theory","volume":"35","author":"Chua","year":"1988","journal-title":"IEEE Trans. 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