{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T18:52:11Z","timestamp":1773082331148,"version":"3.50.1"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2007,4,1]],"date-time":"2007-04-01T00:00:00Z","timestamp":1175385600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2007,4]]},"abstract":"<jats:p>The relationship between continuous-time dynamics and the corresponding discrete schemes, and its generally limited validity, is an important and widely acknowledged field within numerical analysis. In this paper, we propose another, more physical, viewpoint on this topic in order to understand the possible failure of discretisation procedures and the way to fix it. Three basic examples, the logistic equation, the Lotka\u2013Volterra predator\u2013prey model and Newton's law for planetary motion, are worked out. They illustrate the deep difference between continuous-time evolutions and discrete-time mappings, hence shedding some light on the more general duality between continuous descriptions of natural phenomena and discrete numerical computations.<\/jats:p>","DOI":"10.1017\/s0960129507005981","type":"journal-article","created":{"date-parts":[[2007,5,3]],"date-time":"2007-05-03T17:02:05Z","timestamp":1178211725000},"page":"261-276","source":"Crossref","is-referenced-by-count":8,"title":["Discrete-time and continuous-time modelling: some bridges and gaps"],"prefix":"10.1017","volume":"17","author":[{"given":"HUBERT","family":"KRIVINE","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANNICK","family":"LESNE","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JACQUES","family":"TREINER","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2007,4,1]]},"reference":[{"key":"S0960129507005981_N103A3","volume-title":"Le\u00e7ons sur la th\u00e9orie math\u00e9matique de la lutte pour la vie","author":"Volterra","year":"1931"},{"key":"S0960129507005981_N10351","doi-asserted-by":"crossref","unstructured":"Shannon C. (1949) Communication in the presence of noise. Proceedings of the IRE 37 10\u201321. (Reprinted in Proceedings of the IEEE 86 447\u2013457 (1998).)","DOI":"10.1109\/JRPROC.1949.232969"},{"key":"S0960129507005981_N1033A","volume-title":"Deterministic chaos","author":"Schuster","year":"1984"},{"key":"S0960129507005981_N1031D","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492900002282"},{"key":"S0960129507005981_N102FD","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4740-9"},{"key":"S0960129507005981_N10289","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/37\/4\/008"},{"key":"S0960129507005981_N1021E","first-page":"74","article-title":"Sulla teoria di Volterra della lotta per l'esistenza","volume":"7","author":"Kolmogorov","year":"1936","journal-title":"Giornale Istituto Ital. Attuari"},{"key":"S0960129507005981_N103BA","doi-asserted-by":"publisher","DOI":"10.3792\/pjaa.55.78"},{"key":"S0960129507005981_N10119","first-page":"193","article-title":"L'algorithme de Newton-Hooke","volume":"861","author":"Coullet","year":"2004","journal-title":"Bulletin de l'Union des Physiciens"},{"key":"S0960129507005981_N10179","volume-title":"Statistical mechanics of nonequilibrium liquids","author":"Evans","year":"1990"},{"key":"S0960129507005981_N10372","volume-title":"Chaos and integrability in non linear dynamics. An introduction","author":"Tabor","year":"1989"},{"key":"S0960129507005981_N10386","first-page":"13","article-title":"Notice sur la loi que la population suit dans son accroissement","volume":"10","author":"Verhulst","year":"1838","journal-title":"Corresp. Math. et Phys."},{"key":"S0960129507005981_N10165","volume-title":"An introduction to chaotic dynamical systems","author":"Devaney","year":"1989"},{"key":"S0960129507005981_N102AC","doi-asserted-by":"publisher","DOI":"10.1080\/1023619021000000807"},{"key":"S0960129507005981_N102E0","first-page":"617","article-title":"Certain topics in telegraph transmission theory","volume":"47","author":"Nyquist","year":"1928","journal-title":"AIEE Trans."},{"key":"S0960129507005981_N1026C","doi-asserted-by":"publisher","DOI":"10.1038\/261459a0"},{"key":"S0960129507005981_N10142","first-page":"577","article-title":"It\u00e9ration d'endomorphismes et groupe de renormalisation","volume":"287A","author":"Coullet","year":"1978","journal-title":"CR Acad. Sc. Paris"},{"key":"S0960129507005981_N101D0","volume-title":"Differential equations, a dynamical systems approach","author":"Hubbard","year":"1991"},{"key":"S0960129507005981_N102C9","doi-asserted-by":"crossref","DOI":"10.1007\/b98868","volume-title":"Mathematical biology","author":"Murray","year":"2002"},{"key":"S0960129507005981_N10204","volume-title":"Elementary stability and bifurcation theory","author":"Iooss","year":"1981"},{"key":"S0960129507005981_N1023B","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.6.7.410"},{"key":"S0960129507005981_N100FF","volume-title":"Differential equations: A modeling perspective","author":"Borrelli","year":"1998"},{"key":"S0960129507005981_N10193","doi-asserted-by":"publisher","DOI":"10.1007\/BF01020332"},{"key":"S0960129507005981_N101B0","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-05018-7"},{"key":"S0960129507005981_N101EA","volume-title":"Chaos: a program collection for the PC","author":"Korsch","year":"1998"},{"key":"S0960129507005981_N10258","volume-title":"Stability and complexity in model ecosystems","author":"May","year":"1973"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129507005981","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,4,21]],"date-time":"2020-04-21T17:52:59Z","timestamp":1587491579000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129507005981\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,4]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2007,4]]}},"alternative-id":["S0960129507005981"],"URL":"https:\/\/doi.org\/10.1017\/s0960129507005981","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,4]]}}}