{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:40:00Z","timestamp":1760784000854},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2015,8]]},"abstract":"<jats:p> In this paper, we are concerned with positive solutions of a predator\u2013prey model with Crowley\u2013Martin functional response under homogeneous Dirichlet boundary conditions. First, we prove the existence and reveal the structure of the positive solutions by using bifurcation theory. Then, we investigate the uniqueness and stability of the positive solutions for a large key parameter. In addition, we derive some sufficient conditions for the uniqueness of the positive solutions by using some specific inequalities. Moreover, we discuss the extinction and persistence results of time-dependent positive solutions to the system. Finally, we present some numerical simulations to supplement the analytic results in one dimension. <\/jats:p>","DOI":"10.1142\/s0218127415501102","type":"journal-article","created":{"date-parts":[[2015,9,4]],"date-time":"2015-09-04T03:59:52Z","timestamp":1441339192000},"page":"1550110","source":"Crossref","is-referenced-by-count":16,"title":["Qualitative Analysis of a Predator\u2013Prey Model with Crowley\u2013Martin Functional Response"],"prefix":"10.1142","volume":"25","author":[{"given":"Yaying","family":"Dong","sequence":"first","affiliation":[{"name":"School of Mathematics, Northwest University, Xi'an, Shaanxi 710069, P. R. China"}]},{"given":"Shunli","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Northwest University, Xi'an, Shaanxi 710069, P. R. China"}]},{"given":"Shanbing","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, P. R. China"}]},{"given":"Yanling","family":"Li","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Shaanxi Normal University, Xi'an, Shaanxi 710062, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2015,9,3]]},"reference":[{"key":"rf1","volume-title":"Nonlinear Dynamics of Interacting Populations","author":"Bazykin A. D.","year":"1988"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/0517094"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(71)90015-2"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s10910-012-0138-z"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500000895"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2009.09.003"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1137\/0520025"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1093\/imamat\/hxr050"},{"key":"rf9","volume-title":"Nonlinear Parabolic and Elliptic Equations","author":"Pao C. V.","year":"1992"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(95)00058-4"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.04.033"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(71)90030-9"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2005.06.020"},{"key":"rf14","first-page":"459","volume":"36","author":"Shi X. Y.","year":"2011","journal-title":"J. Math. Anal. Appl."},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2009.03.020"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2008.04.054"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2012.04.021"},{"key":"rf18","volume-title":"Introduction to Reaction\u2013Diffusion Equations","author":"Ye Q. X.","year":"1990"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2008.10.024"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.4134\/BKMS.2011.48.3.555"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2012.01.013"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2013.03.064"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127415501102","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:50:58Z","timestamp":1565117458000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127415501102"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,8]]},"references-count":22,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2015,9,3]]},"published-print":{"date-parts":[[2015,8]]}},"alternative-id":["10.1142\/S0218127415501102"],"URL":"https:\/\/doi.org\/10.1142\/s0218127415501102","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,8]]}}}