{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T16:18:17Z","timestamp":1772295497056,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":17,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540347712","type":"print"},{"value":"9783540347743","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2006]]},"DOI":"10.1007\/3-540-34774-7_13","type":"book-chapter","created":{"date-parts":[[2006,8,25]],"date-time":"2006-08-25T19:48:26Z","timestamp":1156535306000},"page":"97-104","source":"Crossref","is-referenced-by-count":3,"title":["Feedback-Mediated Oscillatory Coexistence in the Chemostat"],"prefix":"10.1007","author":[{"given":"Patrick","family":"De Leenheer","sequence":"first","affiliation":[]},{"given":"Sergei S.","family":"Pilyugin","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"13_CR1","first-page":"107","volume":"11","author":"J. Arino","year":"2003","unstructured":"J. Arino, S. S. Pilyugin, and G.S.K. WolkowiczConsiderations on yield, nutrient uptake, cellular growth, and competition in chemostat models, Can. Appl. Math. Quart. 11 (2003), pp. 107\u2013142.","journal-title":"Can. Appl. Math. Quart."},{"key":"13_CR2","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1007\/BF00276918","volume":"12","author":"G. J. Butler","year":"1981","unstructured":"G. J. Butler and P. Waltman, Bifurcation from a limit cycle in a two-predator-one prey ecosystem modeled on a chemostat, J. Math. Biol. 12 (1981), pp. 295\u2013310.","journal-title":"J. Math. Biol."},{"key":"13_CR3","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/BF00305755","volume":"17","author":"G. J. Butler","year":"1983","unstructured":"G. J. Butler, S. B. Hsu, and P. WaltmanCoexistence of competing predators in a chemostat, J. Math. Biol. 17 (1983), pp. 133\u2013151.","journal-title":"J. Math. Biol."},{"key":"13_CR4","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1137\/0145025","volume":"45","author":"G. J. Butler","year":"1985","unstructured":"G. J. Butler, S. B. Hsu, and P. WaltmanA mathematical model of the, chemostat with periodic washout rate, SIAM J. Appl. Math. 45 (1985), pp. 435\u2013449.","journal-title":"SIAM J. Appl. Math."},{"key":"13_CR5","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1137\/0145006","volume":"45","author":"G. J. Butler","year":"1985","unstructured":"G. J. Butler and G.S.K. WolkowiczA mathematical model of the chemostat with general class of functions describing nutrient uptake, SIAM J. Appl. Math. 45 (1985), pp. 138\u2013151.","journal-title":"SIAM J. Appl. Math."},{"key":"13_CR6","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1007\/s00285-002-0170-x","volume":"46","author":"P. Leenheer De","year":"2003","unstructured":"P. De Leenheer and H. L. SmithFeedback control for chemostat models, J. Math. Biol. 46 (2003), pp. 48\u201370.","journal-title":"J. Math. Biol."},{"key":"13_CR7","first-page":"229","volume":"11","author":"P. Leenheer De","year":"2003","unstructured":"P. De Leenheer, B. Li, and H.L. SmithCompetition in the chemostat: some remarks, Can. Appl. Math. Quart. 11 (2003), pp. 229\u2013248.","journal-title":"Can. Appl. Math. Quart."},{"key":"13_CR8","doi-asserted-by":"publisher","first-page":"132","DOI":"10.1006\/jdeq.2000.4041","volume":"171","author":"S.F. Ellermeyer","year":"2001","unstructured":"S.F. Ellermeyer, S.S. Pilyugin, and R. RedhefferPersistence criteria for a chemostat with variable nutrient input, J. Differential Equations 171 (2001), pp. 132\u2013147.","journal-title":"J. Differential Equations"},{"key":"13_CR9","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1016\/j.nonrwa.2004.12.003","volume":"6","author":"J.-L. Gouz\u00e9","year":"2005","unstructured":"J.-L. Gouz\u00e9 and G. RobledoFeedback control for nonmonotone competition, models in the chemostat, Nonlinear Analysis: Real World Applications 6 (2005), pp. 671\u2013690.","journal-title":"Nonlinear Analysis: Real World Applications"},{"key":"13_CR10","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/BF00276091","volume":"18","author":"J. K. Hale","year":"1983","unstructured":"J. K. Hale and A.S. SomolinosCompetition for fluctuating nutrient, J. Math. Biol. 18 (1983), pp. 255\u2013280.","journal-title":"J. Math. Biol."},{"key":"13_CR11","doi-asserted-by":"publisher","first-page":"760","DOI":"10.1137\/0134064","volume":"34","author":"S. B. Hsu","year":"1978","unstructured":"S. B. HsuLimiting behavior of competing species, SIAM J. Appl. Math. 34, (1978), pp. 760\u2013763.","journal-title":"SIAM J. Appl. Math."},{"key":"13_CR12","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/S0025-5564(02)00214-6","volume":"182","author":"S. S. Pilyugin","year":"2003","unstructured":"S. S. Pilyugin and P. WaltmanMultiple limit cycles in the chemostat with, variable yield, Math. Biosci. 182 (2003), pp. 151\u2013166.","journal-title":"Math. Biosci."},{"key":"13_CR13","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1137\/S0036139902418419","volume":"64","author":"S. S. Pilyugin","year":"2003","unstructured":"S. S. Pilyugin and P. WaltmanDivergence criterion for generic planar, systems, SIAM J. Appl. Math. 64 (2003), pp. 81\u201393.","journal-title":"SIAM J. Appl. Math."},{"key":"13_CR14","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1137\/0150049","volume":"50","author":"N.S. Rao","year":"1990","unstructured":"N.S. Rao and E. O. RoxinControlled growth of competing species, SIAM J. Appl. Math. 50 (1990), pp. 853\u2013864.","journal-title":"SIAM J. Appl. Math."},{"key":"13_CR15","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1137\/0140042","volume":"40","author":"H.L. Smith","year":"1981","unstructured":"H.L. SmithCompetitive coexistence in an oscillating chemostat, SIAM J. Appl. Math. 40 (1981), pp. 498\u2013522.","journal-title":"SIAM J. Appl. Math."},{"key":"13_CR16","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511530043","volume-title":"The Theory of the Chemostat","author":"H.L. Smith","year":"1995","unstructured":"H.L. Smith and P. WaltmanThe Theory of the Chemostat, Cambridge University Press, Cambridge, 1995."},{"key":"13_CR17","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1137\/0152012","volume":"48","author":"G.S.K. Wolkowicz","year":"1992","unstructured":"G.S.K. Wolkowicz and Z. Lu, Global dynamics of a mathematical model of, competition in the chemostat: general response functions and differential death rates, SIAM J. Appl. Math. 48 (1992), pp. 222\u2013233.","journal-title":"SIAM J. Appl. Math."}],"container-title":["Lecture Notes in Control and Information Sciences","Positive Systems"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-34774-7_13","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,12]],"date-time":"2019-02-12T02:23:32Z","timestamp":1549938212000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-34774-7_13"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006]]},"ISBN":["9783540347712","9783540347743"],"references-count":17,"URL":"https:\/\/doi.org\/10.1007\/3-540-34774-7_13","relation":{},"ISSN":["0170-8643"],"issn-type":[{"value":"0170-8643","type":"print"}],"subject":[],"published":{"date-parts":[[2006]]}}}