{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,19]],"date-time":"2026-01-19T06:21:10Z","timestamp":1768803670783,"version":"3.49.0"},"reference-count":41,"publisher":"World Scientific Pub Co Pte Ltd","issue":"10","funder":[{"DOI":"10.13039\/501100021856","name":"Ministero dell University della Ricerca","doi-asserted-by":"publisher","award":["2017LSCR4K-003"],"award-info":[{"award-number":["2017LSCR4K-003"]}],"id":[{"id":"10.13039\/501100021856","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p> The paper considers a class of discrete-time cellular neural networks (DT-CNNs) obtained by applying Euler\u2019s discretization scheme to standard CNNs. Let [Formula: see text] be the DT-CNN interconnection matrix which is defined by the feedback cloning template. The paper shows that a DT-CNN is convergent, i.e. each solution tends to an equilibrium point, when [Formula: see text] is symmetric and, in the case where [Formula: see text] is not positive-semidefinite, the step size of Euler\u2019s discretization scheme does not exceed a given bound ([Formula: see text] is the [Formula: see text] unit matrix). It is shown that two relevant properties hold as a consequence of the local and space-invariant interconnecting structure of a DT-CNN, namely: (1)\u00a0the bound on the step size can be easily estimated via the elements of the DT-CNN feedback cloning template only; (2)\u00a0the bound is independent of the DT-CNN dimension. These two properties make DT-CNNs very effective in view of computer simulations and for the practical applications to high-dimensional processing tasks. The obtained results are proved via Lyapunov approach and LaSalle\u2019s Invariance Principle in combination with some fundamental inequalities enjoyed by the projection operator on a convex set. The results are compared with previous ones in the literature on the convergence of DT-CNNs and also with those obtained for different neural network models as the Brain-State-in-a-Box model. Finally, the results on convergence are illustrated via the application to some relevant 2D and 1D DT-CNNs for image processing tasks. <\/jats:p>","DOI":"10.1142\/s0218127423501158","type":"journal-article","created":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T07:39:23Z","timestamp":1693813163000},"source":"Crossref","is-referenced-by-count":2,"title":["Convergence of Discrete-Time Cellular Neural Networks with Application to Image Processing"],"prefix":"10.1142","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0013-9112","authenticated-orcid":false,"given":"Mauro","family":"Di Marco","sequence":"first","affiliation":[{"name":"Department of Information Engineering and Mathematics, University of Siena, Via Roma 56-53100 Siena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mauro","family":"Forti","sequence":"additional","affiliation":[{"name":"Department of Information Engineering and Mathematics, University of Siena, Via Roma 56-53100 Siena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2502-9542","authenticated-orcid":false,"given":"Luca","family":"Pancioni","sequence":"additional","affiliation":[{"name":"Department of Information Engineering and Mathematics, University of Siena, Via Roma 56-53100 Siena, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0234-5999","authenticated-orcid":false,"given":"Alberto","family":"Tesi","sequence":"additional","affiliation":[{"name":"Department of Information Engineering, University of Florence, Via S. 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