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Math. Biol."],"published-print":{"date-parts":[[2025,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    General conditions are established under which reaction-cross-diffusion systems can undergo spatiotemporal pattern-forming instabilities. Recent work has focused on designing systems theoretically and experimentally to exhibit patterns with specific features, but the case of non-diagonal diffusion matrices has yet to be analysed. Here, a framework is presented for the design of general\n                    <jats:italic>n<\/jats:italic>\n                    -component reaction-cross-diffusion systems that exhibit Turing and wave instabilities of a given wavelength. For a fixed set of reaction kinetics, it is shown how to choose diffusion matrices that produce each instability; conversely, for a given diffusion tensor, how to choose linearised kinetics. The theory is applied to several examples including a hyperbolic reaction-diffusion system, two different 3-component models, and a spatio-temporal version of the Ross-Macdonald model for the spread of malaria.\n                  <\/jats:p>","DOI":"10.1007\/s00285-025-02274-1","type":"journal-article","created":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:09:28Z","timestamp":1757617768000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Designing reaction-cross-diffusion systems with Turing and wave instabilities"],"prefix":"10.1007","volume":"91","author":[{"given":"Edgardo","family":"Villar-Sep\u00falveda","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alan R.","family":"Champneys","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9638-7278","authenticated-orcid":false,"given":"Andrew L.","family":"Krause","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,9,11]]},"reference":[{"key":"2274_CR1","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1098\/rstb.1952.0012","volume":"237","author":"AM Turing","year":"1952","unstructured":"Turing AM (1952) The chemical basis of morphogenesis. 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