{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T23:24:17Z","timestamp":1768519457558,"version":"3.49.0"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,3,23]],"date-time":"2023-03-23T00:00:00Z","timestamp":1679529600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The paper presents a solution to the problem related to the reconstruction of parameters in the mathematical model of bacterial colony patterns in a domain with symmetry. The inverse problem consists of determining the value of the diffusion coefficient of active bacteria. The model describing the distribution of active bacteria in a given region, as well as the concentration of the substrate over time is considered. Such a model consists of a system of partial differential equations with appropriate initial-boundary conditions. The finite element method was used to solve the direct problem. However, the Fibonacci search method was used to minimize the functional description of the error of the approximate solution.<\/jats:p>","DOI":"10.3390\/sym15040782","type":"journal-article","created":{"date-parts":[[2023,3,23]],"date-time":"2023-03-23T04:37:28Z","timestamp":1679546248000},"page":"782","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Parameter Estimation in the Mathematical Model of Bacterial Colony Patterns in Symmetry Domain"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7255-6951","authenticated-orcid":false,"given":"Rafa\u0142","family":"Brociek","sequence":"first","affiliation":[{"name":"Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1667-3328","authenticated-orcid":false,"given":"Agata","family":"Wajda","sequence":"additional","affiliation":[{"name":"Institute of Energy and Fuel Processing Technology, 41-803 Zabrze, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2555-9866","authenticated-orcid":false,"given":"Giacomo","family":"Capizzi","sequence":"additional","affiliation":[{"name":"Department of Electrical, Electronics and Informatics Engineering, University of Catania, Viale A. 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