{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,11]],"date-time":"2025-03-11T04:20:39Z","timestamp":1741666839337,"version":"3.38.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2009,3,1]],"date-time":"2009-03-01T00:00:00Z","timestamp":1235865600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2009,3]]},"abstract":"<jats:p> We consider a spatially structured predator\u2013prey model where fast migrations occur inside a given spatial domain, while slow predator\u2013prey interactions prescribe the demographic evolution. The unknowns of our model are the numbers of predators and prey at each time t and each site x of the domain. In the idealized limit where migrations are infinitely fast, we show one can approximate the global dynamics using the mere two unknowns corresponding to the total number of preys and predators, irrespective of their respective spatial repartition. Besides, the error term induced by this approximation can be made exponentially small with respect to the natural asymptotic parameter. <\/jats:p><jats:p> In doing so, we completely characterize how migrations do modify both the qualitative and quantitative properties of the global demography. <\/jats:p><jats:p> Our analysis relies on a convenient version of the central manifold theorem, in conjunction with a spectral gap estimate on the involved migration operator. <\/jats:p>","DOI":"10.3233\/asy-2008-0905","type":"journal-article","created":{"date-parts":[[2019,11,30]],"date-time":"2019-11-30T00:04:20Z","timestamp":1575072260000},"page":"125-175","source":"Crossref","is-referenced-by-count":3,"title":["A reduced model for spatially structured predator\u2013prey systems with fast spatial migrations and slow demographic evolutions"],"prefix":"10.1177","volume":"61","author":[{"given":"Fran\u00e7ois","family":"Castella","sequence":"first","affiliation":[{"name":"IRMAR & IRISA, Universit\u00e9 de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France. E-mail: francois.castella@univ-rennes1.fr"}]},{"given":"Jean-Philippe","family":"Hoffbeck","sequence":"additional","affiliation":[{"name":"Lyc\u00e9e du Hainaut, 1 Avenue Villars, 59300 Valenciennes, France. E-mail: jean-philippe.hoffbeck@wanadoo.fr"}]},{"given":"Yvan","family":"Lagadeuc","sequence":"additional","affiliation":[{"name":"UMR CNRS 6553 Ecobio et IFR\/FR Caren, Universit\u00e9 de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France. E-mail: yvan.lagadeuc@univ-rennes1.fr"}]}],"member":"179","published-online":{"date-parts":[[2009,3,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0905","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2008-0905","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,10]],"date-time":"2025-03-10T14:59:47Z","timestamp":1741618787000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2008-0905"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2009,3]]}},"alternative-id":["10.3233\/ASY-2008-0905"],"URL":"https:\/\/doi.org\/10.3233\/asy-2008-0905","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"type":"print","value":"0921-7134"},{"type":"electronic","value":"1875-8576"}],"subject":[],"published":{"date-parts":[[2009,3]]}}}