{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:55:22Z","timestamp":1760151322577,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,9]],"date-time":"2022-03-09T00:00:00Z","timestamp":1646784000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS 1839993, DMS 1715044"],"award-info":[{"award-number":["DMS 1839993, DMS 1715044"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The Trojan Y Chromosome Strategy (TYC) is the only genetic biological control method in practice in North America for controlling invasive populations with an XX\u2013XY sex determinism. Herein a modified organism, that is a supermale or feminised supermale, is introduced into an invasive population to skew the sex ratio over time, causing local extinction. We consider the three species TYC reaction diffusion model, and show that introduction of supermales above certain thresholds, and for certain initial data, solutions can blow-up in finite time. Thus, in order to have biologically meaningful solutions, one needs to restrict parameter and initial data regimes, in TYC type models.<\/jats:p>","DOI":"10.3390\/axioms11030120","type":"journal-article","created":{"date-parts":[[2022,3,9]],"date-time":"2022-03-09T11:30:38Z","timestamp":1646825438000},"page":"120","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On Large and Small Data Blow-Up Solutions in the Trojan Y Chromosome Model"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6398-6845","authenticated-orcid":false,"given":"Eric M.","family":"Takyi","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science, Ursinus College, Collegeville, PA 19426, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthew A.","family":"Beauregard","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Stephen F. Austin State University, Nacogdoches, TX 75962, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Griffin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Iowa State University, Ames, IA 50011, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Landrey","family":"Bobo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Texas, Austin, TX 78712, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rana D.","family":"Parshad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Iowa State University, Ames, IA 50011, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1073\/pnas.0504272102","article-title":"Spread Dynamics of invasive species","volume":"103","author":"Arim","year":"2006","journal-title":"Proc. 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