{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T13:41:13Z","timestamp":1777902073627,"version":"3.51.4"},"reference-count":17,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2004,2,1]],"date-time":"2004-02-01T00:00:00Z","timestamp":1075593600000},"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":["SIMULATION"],"published-print":{"date-parts":[[2004,2]]},"abstract":"<jats:p>Differential inclusions (DIs) represent an important extension of differential equations. The other term used for DI is differential equations with a set-valued right-hand side. This tool can be used when the model reveals uncertainty that is given in terms of limits or permissible sets rather than random variables. A model of stock exchange dynamics with uncertain information and a model with an ideal predictor are presented to illustrate possible applications. The ideal predictor problem is equivalent to the problem of passing the information from the future to the present, or traveling into the past to use the present information and change the model trajectory. It is shown that the uncertainty over the future can be simulated using differential inclusions. A differential inclusion solver is described.<\/jats:p>","DOI":"10.1177\/0037549704042858","type":"journal-article","created":{"date-parts":[[2004,5,27]],"date-time":"2004-05-27T22:29:13Z","timestamp":1085696953000},"page":"87-100","source":"Crossref","is-referenced-by-count":11,"title":["Continuous Simulation, Differential Inclusions, Uncertainty, and Traveling in Time"],"prefix":"10.1177","volume":"80","author":[{"given":"Stanislaw","family":"Raczynski","sequence":"first","affiliation":[{"name":"Universidad Panamericana Augusto Rodin 498, 03910 Mexico D.F."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2004,2,1]]},"reference":[{"key":"atypb1","unstructured":"[1] Klir, G. J., and T. A. Folger. 1988. Fuzzy sets, uncertainty, and information. Englewood Cliffs, NJ: Prentice Hall ."},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"[3] Raczynski, S. 1986. Some remarks on nonconvex optimal control . Journal of Mathematical Analysis and Applications 18: 24-37 .","DOI":"10.1016\/0022-247X(86)90287-8"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(84)90295-6"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"[5] Marchaud, A. 1934. Sur les champs de demi-dro\u00edtes et les \u00e9quations deff\u00e9rielles du premier ordre. Bulletin de la Societ\u00c8 Math\u00c8matique de France 62:1-38.","DOI":"10.24033\/bsmf.1211"},{"key":"atypb6","unstructured":"[6] Zaremba, S. K. 1936. Sur les \u00e9quations au paratingent. Bulletin de la Societ\u00c8 Math\u00c8matique de France 60:139-60."},{"key":"atypb7","unstructured":"[7] Wazewski, T. 1961. Sur une condition equivalente a l\u2019equation au contingent. Bulletin de l\u2019Academie Polonaise des Sciences: Serie des sciences math\u00c8matiques, astronomiques et physiques 9 (12):865-7."},{"key":"atypb8","unstructured":"[8] Wazewski, T. 1962. Sur une genralisation de la notion des solutions d\u2019une equation au contingent. Bulletin de l\u2019Academie Polonaise des Sciences: Serie des sciences math\u00c8matiques, astronomiques et physiques 10 (1):11-5."},{"key":"atypb9","unstructured":"[9] Wazewski, T. 1962. Sur les systemes de commande non lineaires dont le contredomaine de commande n\u2019est pas forcement convexe. Bulletin de l\u2019Academie Polonaise des Sciences: Serie des sciences math\u00c8matiques, astronomiques et physiques, in press."},{"key":"atypb10","unstructured":"[10] Pontriagin, L. S. 1962. The mathematical theory of optimal processes. New York: Wiley Interscience ."},{"key":"atypb11","unstructured":"[11] Lee, E. B., and L. Markus. 1967. Foundations of optimal control theory. New York: John Wiley ."},{"key":"atypb12","unstructured":"[12] Raczynski, S. 1996. Differential inclusions in system simulation . Transactions of the Society for Computer Simulation 13 (1): 47-54 ."},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"[13] Aubin, J. P., and A. Cellina. 1984. Differential inclusions. New York: Springer-Verlag .","DOI":"10.1007\/978-3-642-69512-4"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022031423159"},{"key":"atypb15","unstructured":"[15] Minsky, H. 1982. The financial instability hypothesis: An interpretation of Keynes and alternative \u201cstandard theory.\u201d In Recession and economic policy. Sussex, UK: Wheatsheaf ."},{"key":"atypb16","unstructured":"[16] Goodwin, R. M. 1967. A growth cycle. In Capitalism and economic growth, edited by C.H. Feinstein. Cambridge, UK: Cambridge University Press ."},{"key":"atypb17","unstructured":"[17] Glassman, K. J. 1998. Trying to crack the code; computer models lag as stock pickers. The Washington Post, 15 October."}],"container-title":["SIMULATION"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549704042858","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/0037549704042858","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T11:18:27Z","timestamp":1777634307000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/0037549704042858"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,2]]},"references-count":17,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2004,2]]}},"alternative-id":["10.1177\/0037549704042858"],"URL":"https:\/\/doi.org\/10.1177\/0037549704042858","relation":{},"ISSN":["0037-5497","1741-3133"],"issn-type":[{"value":"0037-5497","type":"print"},{"value":"1741-3133","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,2]]}}}