{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:53:17Z","timestamp":1760241197885,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2019,12,23]],"date-time":"2019-12-23T00:00:00Z","timestamp":1577059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Bielsko-Biala","award":["511\/100\/4\/10\/00"],"award-info":[{"award-number":["511\/100\/4\/10\/00"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Biosensors and immunosensors show an increasing attractiveness when developing current cheap and fast monitoring and detecting devices. In this work, a model of immunosensor in a class of delayed lattice differential equations is offered and studied. The spatial operator describes symmetric diffusion processes of antigenes between pixels. The main results are devoted to the qualitative research of the model. The conditions of global asymptotic stability, which are constructed with the help of Lyapunov functionals, determine a lower estimate of the time of immune response. Nonlinear analysis of the model is performed with help of a series of numerical characteristics including autocorrelation function, mutual information, embedding, and correlation dimensions, sample entropy, the largest Lyapunov exponents. We consider the influence of both symmetric and unsymmetric diffusion of antigens between pixels on the qualitative behavior of the system. The outcomes are verified with the help of numerical simulation in cases of     4 \u00d7 4    - and     16 \u00d7 16    - arrays of immunopixels.<\/jats:p>","DOI":"10.3390\/sym12010040","type":"journal-article","created":{"date-parts":[[2019,12,24]],"date-time":"2019-12-24T05:56:15Z","timestamp":1577166975000},"page":"40","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Global Asymptotic Stability and Nonlinear Analysis of the Model of the Square Immunopixels Array Based on Delay Lattice Differential Equations"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5622-1038","authenticated-orcid":false,"given":"Vasyl","family":"Martsenyuk","sequence":"first","affiliation":[{"name":"Department of Computer Science and Automatics, University of Bielsko-Biala, 43-309 Bielsko-Bia\u0142a, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8846-332X","authenticated-orcid":false,"given":"Miko\u0142aj","family":"Karpinski","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Automatics, University of Bielsko-Biala, 43-309 Bielsko-Bia\u0142a, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stanislaw","family":"Rajba","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Automatics, University of Bielsko-Biala, 43-309 Bielsko-Bia\u0142a, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joanna","family":"Nikodem","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Automatics, University of Bielsko-Biala, 43-309 Bielsko-Bia\u0142a, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kornel","family":"Warwas","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Automatics, University of Bielsko-Biala, 43-309 Bielsko-Bia\u0142a, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lukasz","family":"Wieclaw","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Automatics, University of Bielsko-Biala, 43-309 Bielsko-Bia\u0142a, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tomasz","family":"Gancarczyk","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Automatics, University of Bielsko-Biala, 43-309 Bielsko-Bia\u0142a, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"19","DOI":"10.15244\/pjoes\/28352","article-title":"Enzyme-Based Fluorescent Biosensors and Their Environmental, Clinical and Industrial Applications","volume":"24","year":"2015","journal-title":"Pol. 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