{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:10:44Z","timestamp":1762521044455},"reference-count":10,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2006,3,1]],"date-time":"2006-03-01T00:00:00Z","timestamp":1141171200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Jrl Syst Sci &amp; Complex"],"published-print":{"date-parts":[[2006,3]]},"DOI":"10.1007\/s11424-006-0137-x","type":"journal-article","created":{"date-parts":[[2006,4,4]],"date-time":"2006-04-04T02:04:54Z","timestamp":1144116294000},"page":"137-144","source":"Crossref","is-referenced-by-count":4,"title":["Ultimate Stability of a Type of Characteristic Equation with Delay Dependent Parameters"],"prefix":"10.1007","volume":"19","author":[{"given":"Jianquan","family":"Li","sequence":"first","affiliation":[]},{"given":"Zhien","family":"Ma","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"137_CR1","volume-title":"Delay Differential Equations with Applications in Population Dynamics","author":"Y. Kuang","year":"1993","unstructured":"Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, 1993."},{"key":"137_CR2","doi-asserted-by":"crossref","first-page":"592","DOI":"10.1016\/0022-247X(82)90243-8","volume":"86","author":"K. L. Cooke","year":"1982","unstructured":"K. L. Cooke and Z. Grossman, Discrete delay, distributed delay and stability switches, J. math. Anal. Appl., 1982, 86: 592\u2013627.","journal-title":"J. math. Anal. Appl."},{"key":"137_CR3","first-page":"77","volume":"29","author":"K. L. Cooke","year":"1986","unstructured":"K. L. Cooke and P. van den Driessche, On zeros of some transcendental equation, Funkcial. Evac., 1986, 29: 77\u201390.","journal-title":"Funkcial. Evac."},{"key":"137_CR4","unstructured":"Qing Huang and Zhien Ma, On stability of some transcendental equation, Ann. of Diff. Eqs., 1990, 6: 21\u201331."},{"key":"137_CR5","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1137\/0152048","volume":"52","author":"W. G. Aiello","year":"1992","unstructured":"W. G. Aiello, H. I. Freedman and J. Wu, A model of stage structured population growth with density dependent time delay, SIAM J. Apl. Math., 1992, 52: 855\u2013569.","journal-title":"SIAM J. Apl. Math."},{"key":"137_CR6","doi-asserted-by":"crossref","first-page":"1231","DOI":"10.1016\/j.mcm.2004.06.004","volume":"39","author":"J. Li","year":"2004","unstructured":"J. Li and Z. Ma, Global analysis of SIS epidemic models with variable table population size, Mathematical and Computer Modelling, 2004, 39: 1231\u20131242.","journal-title":"Mathematical and Computer Modelling"},{"key":"137_CR7","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1007\/s002850050194","volume":"39","author":"K. L. Cooke","year":"1999","unstructured":"K. L. Cooke, P. van den Driessche and X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models, J. Math. Biol., 1999, 39: 332\u2013352.","journal-title":"J. Math. Biol."},{"key":"137_CR8","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1007\/s002850050051","volume":"35","author":"K. L. Cooke","year":"1996","unstructured":"K. L. Cooke and P. van den Driessche, Analysis of an SEIS epidemic model with two delays, J. Math. Biol., 1996, 35: 240\u2013260.","journal-title":"J. Math. Biol."},{"key":"137_CR9","doi-asserted-by":"crossref","first-page":"1144","DOI":"10.1137\/S0036141000376086","volume":"33","author":"E. Beretta","year":"2002","unstructured":"E. Beretta and Y. Kuang, Geometric stability switch criteria in delay differential systems with delay dependent parameters, SIAM J. Math. Anal., 2002, 33: 1144\u20131165.","journal-title":"SIAM J. Math. Anal."},{"key":"137_CR10","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1016\/j.nonrwa.2003.06.001","volume":"5","author":"J. Li","year":"2004","unstructured":"J. Li and Z. Ma, Stability switches in a class of characteristic equations with delay-dependent parameters, Nonlinear Analysis: Real World Applications, 2004, 5: 389\u2013408.","journal-title":"Nonlinear Analysis: Real World Applications"}],"container-title":["Journal of Systems Science and Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-006-0137-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11424-006-0137-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11424-006-0137-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T14:53:54Z","timestamp":1559400834000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11424-006-0137-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,3]]}},"alternative-id":["137"],"URL":"https:\/\/doi.org\/10.1007\/s11424-006-0137-x","relation":{},"ISSN":["1009-6124","1559-7067"],"issn-type":[{"value":"1009-6124","type":"print"},{"value":"1559-7067","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,3]]}}}