{"id":17112,"date":"2023-05-04T10:30:57","date_gmt":"2023-05-04T07:30:57","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=17112"},"modified":"2023-05-17T11:34:52","modified_gmt":"2023-05-17T08:34:52","slug":"porivnyannya-rezultativ-chyselnogo-analizu-modelyuvannya-kiberfizychnyh-biosensornyh-system","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=17112","title":{"rendered":"\u041f\u043e\u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0456\u0432 \u0447\u0438\u0441\u0435\u043b\u044c\u043d\u043e\u0433\u043e \u0430\u043d\u0430\u043b\u0456\u0437\u0443 \u043c\u043e\u0434\u0435\u043b\u044e\u0432\u0430\u043d\u043d\u044f \u043a\u0456\u0431\u0435\u0440\u0444\u0456\u0437\u0438\u0447\u043d\u0438\u0445 \u0431\u0456\u043e\u0441\u0435\u043d\u0441\u043e\u0440\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c"},"content":{"rendered":"

<\/p>\n

\u041f\u041e\u0420\u0406\u0412\u041d\u042f\u041d\u041d\u042f \u0420\u0415\u0417\u0423\u041b\u042c\u0422\u0410\u0422\u0406\u0412 \u0427\u0418\u0421\u0415\u041b\u042c\u041d\u041e\u0413\u041e \u0410\u041d\u0410\u041b\u0406\u0417\u0423 \u041c\u041e\u0414\u0415\u041b\u042e\u0412\u0410\u041d\u041d\u042f \u041a\u0406\u0411\u0415\u0420\u0424\u0406\u0417\u0418\u0427\u041d\u0418\u0425 \u0411\u0406\u041e\u0421\u0415\u041d\u0421\u041e\u0420\u041d\u0418\u0425 \u0421\u0418\u0421\u0422\u0415\u041c<\/p>\n

COMPARISON OF RESULTS OF NUMERICAL ANALYSIS OF SIMULATION OF CYBERPHYSICAL BIOSENSOR SYSTEMS<\/p>\n

\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 202-212. \u041d\u043e\u043c\u0435\u0440: \u21162, 2023 (319)\u00a0<\/strong> \"\"<\/a>
\n\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u041c\u0410\u0420\u0426\u0415\u041d\u042e\u041a \u0412\u0410\u0421\u0418\u041b\u042c
\n\u0423\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0432 \u0411\u0454\u043b\u044c\u0441\u044c\u043a\u043e-\u0411\u044f\u043b\u0456\u0439, \u041f\u043e\u043b\u044c\u0449\u0430
\nhttps:\/\/orcid.org\/0000-0001-5622-1038<\/a>
\ne-mail: vmartsenyuk@ath.bielsko.pl<\/a>
\n\u0410\u041d\u0414\u0420\u0423\u0429\u0410\u041a \u0406\u0413\u041e\u0420
\n\u041b\u0443\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442
\nhttps:\/\/orcid.org\/0000-0002-8751-4420<\/a>
\ne-mail: 9000@lntu.edu.ua
\n\u041a\u0406\u0422 \u041d\u0410\u0422\u0410\u041b\u0406\u042f
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406\u0432\u0430\u043d\u0430 \u041f\u0443\u043b\u044e\u044f
\nhttps:\/\/orcid.org\/0000-0002-9096-4393<\/a>
\ne-mail: natkakooo@gmail.com<\/a>
\n\u041a\u0420\u0410\u0412\u0427\u0418\u041a \u042e\u0420\u0406\u0419
\n\u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442
\nhttps:\/\/orcid.org\/0000-0002-2780-5605<\/a>
\ne-mail: yurii_kravchyk@khmnu.edu.ua<\/a>
\n\u0421\u0412\u0415\u0420\u0421\u0422\u042e\u041a \u0410\u041d\u0414\u0420\u0406\u0419
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u043c\u0435\u0434\u0438\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406.\u042f. \u0413\u043e\u0440\u0431\u0430\u0447\u0435\u0432\u0441\u044c\u043a\u043e\u0433\u043e
\nhttps:\/\/orcid.org\/0000-0001-8644-0776<\/a>
\ne-mail: sverstyuk@tdmu.edu.ua<\/a>
\n\u041f\u0410\u041b\u042f\u041d\u0418\u0426\u042f \u042e\u0420\u0406\u0419
\n\u0422\u0435\u0440\u043d\u043e\u043f\u0456\u043b\u044c\u0441\u044c\u043a\u0438\u0439 \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406\u0432\u0430\u043d\u0430 \u041f\u0443\u043b\u044e\u044f
\nhttps:\/\/orcid.org\/0000-0002-8710-953X<\/a>
\ne-mail: palyanytsa_y@tntu.edu.ua<\/a>
\nVASYL MARTSENYUK
\nUniversity of Bielsko-Biala, Poland
\nIGOR ANDRUSHCHAK
\nLutsk National Technical University
\nNATALIIA KOZODII
\nTernopil Ivan Pului National Technical University
\nYURII KRAVCHYK
\nKhmelnytskyi National University
\nANDRIY\u00a0SVERSTIUK
\nHorbachevsky Ternopil National Medical University
\nYURI PALANIZA
\nTernopil Ivan Pului National Technical University
\nDOI:<\/strong>\u00a0https:\/\/www.doi.org\/10.31891\/2307-5732-2023-319-1-202-212<\/a><\/p>\n

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\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u0440\u0456\u0437\u043d\u0438\u0446\u0435\u0432\u0456 \u0440\u0456\u0432\u043d\u044f\u043d\u043d\u044f, \u043f\u0440\u044f\u043c\u043e\u043a\u0443\u0442\u043d\u0430 \u0440\u0435\u0448\u0456\u0442\u043a\u0430, \u0433\u0435\u043a\u0441\u0430\u0433\u043e\u043d\u0430\u043b\u044c\u043d\u0430 \u0440\u0435\u0448\u0456\u0442\u043a\u0430, \u043a\u0456\u0431\u0435\u0440\u0444\u0456\u0437\u0438\u0447\u043d\u0430 \u0431\u0456\u043e\u0441\u0435\u043d\u0441\u043e\u0440\u043d\u0430 \u0441\u0438\u0441\u0442\u0435\u043c\u0430, \u0441\u0442\u0456\u0439\u043a\u0456\u0441\u0442\u044c \u043c\u043e\u0434\u0435\u043b\u0456.<\/p>\n

\u00a0<\/strong>\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u00a0\u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

The article compares the results of numerical modeling of mathematical models of cyber-physical biosensor systems using lattice difference equations with time delay on hexagonal and rectangular lattices. The main attention is paid to the mathematical description of the dynamics of a discrete population in combination with the dynamic logic of the studied models. Lattice difference equations with delay are proposed for modeling the antigen-antibody interaction in hexagonal and rectangular biopixels. Similar to the diffusion phenomenon, spatial operators are considered to model the interaction between biopixels. The paper compares the results of numerical modeling of processes occurring in biopixels of cyberphysical biosensor systems in the form of phase plane images and lattice images of the probability of antigen-antibody bonds. Based on the obtained experimental results, a comparative analysis of the stability of mathematical models was carried out using lattice difference equations on hexagonal and rectangular lattices for cyberphysical biosensors.
\nKeywords:<\/strong> difference equations, rectangular lattice, hexagonal lattice, cyber-physical biosensor systems, stability of the model<\/p>\n

<\/h4>\n

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