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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2025,4]]},"abstract":"<jats:p> In this work, the influences of geometry and domain size on spatiotemporal pattern formation are investigated to establish the parameter spaces for a cross-diffusive reaction\u2013diffusion model on an annulus. By applying the linear stability theory, we derive the conditions which can give rise to Turing, Hopf and transcritical types of diffusion-driven instabilities. We explore whether the selection of a sufficiently large domain size, together with the appropriate selection of parameters, can give rise to the development of patterns on nonconvex geometries, e.g. annulus. Hence, the key research methodology and outcomes of our studies include a complete analytical exploration of the spatiotemporal dynamics in an activator-depleted reaction\u2013diffusion system; a linear stability analysis to characterize the dual roles of cross-diffusion and domain size of pattern formation on an annulus region; the derivation of the instability conditions through the lower and upper bounds of the domain size; the full classification of the model parameters; and a demonstration of how cross-diffusion relaxes the general conditions for the reaction\u2013diffusion system to exhibit pattern formation. To validate the theoretical findings and predictions, we employ the finite element method to reveal the spatial and spatiotemporal patterns in the dynamics of the cross-diffusive reaction\u2013diffusion system within a two-dimensional annular domain. These observed patterns resemble those found in ring-shaped cross-sectional scans of hypoxic tumors. Specifically, the cross-section of an actively invasive region in a hypoxic tumor can be effectively approximated by an annulus. <\/jats:p>","DOI":"10.1142\/s0218127425500518","type":"journal-article","created":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T01:36:31Z","timestamp":1742175391000},"source":"Crossref","is-referenced-by-count":1,"title":["Parameter Spaces for Cross-Diffusive-Driven Instability in a Reaction\u2013Diffusion System on an Annular Domain"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4442-9151","authenticated-orcid":false,"given":"Gulsemay","family":"Yigit","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Engineering and Natural Sciences, Bah\u00e7e\u015fehir University, Istanbul, Turkey"},{"name":"Department of Mathematics, The University of British Columbia, Mathematics Building, 1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0991-4031","authenticated-orcid":false,"given":"Wakil","family":"Sarfaraz","sequence":"additional","affiliation":[{"name":"Corndel Limited, 410 Highgate Studios, 53-79 Highgate Road, London NW5 1TL, UK"},{"name":"School of ICT, Bahrain Polytechnic, PO Box 33349, Isa Town, Bahrain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8326-1593","authenticated-orcid":false,"given":"Raquel","family":"Barreira","sequence":"additional","affiliation":[{"name":"Escola Superior de Tecnologia de Set\u00fabal, Instituto Polit\u00e9cnico de Set\u00fabal, Campus do IPS Estefanilha, 2914-508 Set\u00fabal, Portugal"},{"name":"Centro de Matem\u00e1tica, Aplica\u00e7\u00f5es Fundamentais e Investiga\u00e7\u00e3o Operacional (CMAFcIO), Faculdade de Ci\u00eancias, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9511-8903","authenticated-orcid":false,"given":"Anotida","family":"Madzvamuse","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of British Columbia, Mathematics Building, 1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2"},{"name":"Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0132, South Africa"},{"name":"Department of Mathematics and Applied Mathematics, University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa"},{"name":"Department of Mathematics and Computational Science, University of Zimbabwe, Mount Pleasant, Harare, Zimbabwe"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,3,14]]},"reference":[{"key":"S0218127425500518BIB001","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/21\/11\/R05"},{"key":"S0218127425500518BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-011-0401-0"},{"key":"S0218127425500518BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218202522500166"},{"key":"S0218127425500518BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0"},{"key":"S0218127425500518BIB005","doi-asserted-by":"publisher","DOI":"10.1063\/1.5135069"},{"key":"S0218127425500518BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.cels.2015.10.002"},{"key":"S0218127425500518BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2019.122023"},{"key":"S0218127425500518BIB009","series-title":"Graduate Studies in Mathematics","volume-title":"Partial Differential Equations","volume":"19","author":"Evans L. 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