{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:35:00Z","timestamp":1787322900796,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>The so-called DNSS points of indifference are of interest because they give decision makers in optimal control problems a choice between following either of two or more trajectories while still achieving optimality. Usually they are described in terms of initial conditions, so that if the system starts at a DNSS point, the decision maker can proceed in either of two or more directions. Here we present a model that has an entire curve of indifference points away from which the decision maker can move in only one direction but does so by choosing either of two trajectories that initially coincide in the state space but later diverge, approaching different long-run steady states.<\/jats:p>","DOI":"10.1137\/080719741","type":"journal-article","created":{"date-parts":[[2010,3,10]],"date-time":"2010-03-10T18:14:29Z","timestamp":1268244869000},"page":"3698-3707","source":"Crossref","is-referenced-by-count":18,"title":["Keeping Options Open: an Optimal Control Model with Trajectories That Reach a DNSS Point in Positive Time"],"prefix":"10.1137","volume":"48","author":[{"given":"Irmgard","family":"Zeiler","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jonathan P.","family":"Caulkins","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dieter","family":"Grass","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gernot","family":"Tragler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,3,10]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0531(83)90081-9"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00933297"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00934454"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.2307\/1914229"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-1889(01)00070-7"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-007-9180-6"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1287\/opre.49.3.352.11215"},{"key":"R8","unstructured":"I. Zeiler,\n                      Optimal Dynamic Control with DNSS Curves: Multiple Equilibria in Epidemic Models of HIV\/AIDS and Illicit Drug Use\n                      , Ph.D. thesis, Faculty of Mathematics and Geoinformation, Vienna University of Technology, Vienna, Austria, 2007."},{"key":"R9","doi-asserted-by":"crossref","unstructured":"D. Grass, J. P. Caulkins, G. Feichtinger, G. Tragler, and D. A. Behrens,\n                      Optimal Control of Nonlinear Processes: With Applications in Drugs, Corruption, and Terror\n                      , Springer, Heidelberg, 2008.","DOI":"10.1007\/978-3-540-77647-5"},{"key":"R10","unstructured":"R. M. Anderson and R. M. May,\n                      Infectious Diseases of Humans: Dynamics and Control\n                      , Oxford Science Publications, Oxford University Press, Oxford, UK, 1991."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1287\/opre.37.2.198"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1093\/imammb\/18.3.225"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1093\/imammb\/13.3.175"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1007\/BF00163880"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/s002850100087"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1093\/imammb\/13.3.151"},{"key":"R17","doi-asserted-by":"crossref","unstructured":"G. Feichtinger and R. F. Hartl,\n                      Optimale Kontrolle \u00d6konomischer Prozesse\u2014Anwendungen des Maximumsprinzips in den Wirtschaftswissenschaften\n                      , Walter de Gruyter, Berlin, 1986.","DOI":"10.1515\/9783110856149"},{"key":"R18","doi-asserted-by":"crossref","unstructured":"D. Leonard and N. V. Long,\n                      Optimal Control Theory and Static Optimization in Economics\n                      , Cambridge University Press, Cambridge, UK, 1992.","DOI":"10.1017\/CBO9781139173551"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008772604955"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1002\/oca.696"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011925332503"},{"key":"R22","unstructured":"R. A. Howard,\n                      Decision analysis: Applied decision theory\n                      , in Proceedings of the Fourth International Conference on Operations Research, D.B. Hertz and J. Melese, eds., Wiley, New York, 1996, pp. 55\u201371."},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/0329068"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-96-01577-2"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080719741","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:32:33Z","timestamp":1787319153000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080719741"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":24,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080719741"],"URL":"https:\/\/doi.org\/10.1137\/080719741","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}