{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:38:57Z","timestamp":1760143137149,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,18]],"date-time":"2024-01-18T00:00:00Z","timestamp":1705536000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003336","name":"Bulgarian National Science Fund","doi-asserted-by":"publisher","award":["KP-06-PN 46-7"],"award-info":[{"award-number":["KP-06-PN 46-7"]}],"id":[{"id":"10.13039\/501100003336","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We analyze a mathematical model of the effects of soil contamination by heavy metals, which is expressed as systems of nonlinear ordinary differential equations (ODEs). The model is based on the symmetry dynamics of heavy metals soil\u2013plant interactions. We aim to study this symmetric process and its long-term behavior, as well as to discuss the role of two crucial parameters, namely the flux of the hydrogen protons to the soil in rainfall events W(t), and the available water for roots p(t). We study the boundedness and positivity of the solution. Further, a parameter identification analysis of the model is presented. Numerical experiments with synthetic and realistic data of honeybee population are discussed.<\/jats:p>","DOI":"10.3390\/sym16010110","type":"journal-article","created":{"date-parts":[[2024,1,18]],"date-time":"2024-01-18T03:50:56Z","timestamp":1705549856000},"page":"110","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Analysis of the Transfer Dynamics of Heavy Metals from Soil to Plant and Application to Contamination of Honey"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4816-2837","authenticated-orcid":false,"given":"Atanas","family":"Atanasov","sequence":"first","affiliation":[{"name":"Department of Agricultural Machinery, Agrarian Industrial Faculty, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9826-9603","authenticated-orcid":false,"given":"Slavi","family":"Georgiev","sequence":"additional","affiliation":[{"name":"Department of Informational Modeling, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. Georgi Bonchev Str., 1113 Sofia, Bulgaria"},{"name":"Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0684-8574","authenticated-orcid":false,"given":"Lubin","family":"Vulkov","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1016\/j.ecolmodel.2010.01.003","article-title":"The dynamics of heavy metals in plant\u2013soil interactions","volume":"221","author":"Guala","year":"2010","journal-title":"Ecol. Model."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"C\u00e2rdei, P., Tudora, C., Vl\u0103du\u021b, V., Pruteanu, M.A., G\u0103deanu, I., Cujbescu, D., Bordean, D.-M., Ungureanu, N., Ipate, G., and Cristea, O.D. (2021). Mathematical model to simulate the transfer of heavy metals from soil to plant. Sustainability, 13.","DOI":"10.3390\/su13116157"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1006\/tpbi.1993.1002","article-title":"The interaction between soil acidity and forest dynamics: A simple-model exhibiting catastrophic behavior","volume":"43","author":"Gatto","year":"1993","journal-title":"Theor. Popul. Biol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1303","DOI":"10.2136\/sssaj1989.03615995005300050001x","article-title":"Two-site\/region models for pesticidies transport and degradiation: Theoretical development and analytical solutions","volume":"53","author":"Wagent","year":"1989","journal-title":"Soil Sci. Soc. Am. 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Inverse and Ill-Posed Problems, De Gruyter.","DOI":"10.1515\/9783110224016"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/110\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:49:21Z","timestamp":1760104161000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/1\/110"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,18]]},"references-count":18,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["sym16010110"],"URL":"https:\/\/doi.org\/10.3390\/sym16010110","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2024,1,18]]}}}