{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T12:07:45Z","timestamp":1762430865423,"version":"3.37.3"},"reference-count":11,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11101117"],"award-info":[{"award-number":["11101117"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>A delayed predator-prey system with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of the feasible equilibria of the system is addressed and the existence of a Hopf bifurcation at the coexistence equilibrium is established. By means of persistence theory on infinite dimensional systems, it is proved that the system is permanent. By using Lyapunov functions and the LaSalle invariant principle, the global stability of each of the feasible equilibria of the model is discussed. Numerical simulations are carried out to illustrate the main theoretical results.<\/jats:p>","DOI":"10.1155\/2014\/431671","type":"journal-article","created":{"date-parts":[[2014,2,26]],"date-time":"2014-02-26T01:08:57Z","timestamp":1393376937000},"page":"1-10","source":"Crossref","is-referenced-by-count":3,"title":["Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure"],"prefix":"10.1155","volume":"2014","author":[{"given":"Lingshu","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanghui","family":"Feng","sequence":"additional","affiliation":[{"name":"Department of Basic Courses, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139993252839"},{"first-page":"253","volume-title":"Global dynamics of a population model with stage structure for predator","year":"1997","key":"9"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(97)00056-4"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-002-0234-2"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-011-0096-1"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2010.12.029"},{"key":"6","first-page":"3","volume":"45","year":"1965","journal-title":"Memoirs of the Entomological Society of Canada"},{"volume":"191","year":"1993","series-title":"Mathematics in Science and Engineering","key":"7"},{"volume":"41","year":"1981","series-title":"London Mathematical Society Lecture Note Series","key":"5"},{"year":"1977","key":"3"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1137\/0520025"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/431671.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/431671.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/431671.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,18]],"date-time":"2016-08-18T15:52:27Z","timestamp":1471535547000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/431671\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":11,"alternative-id":["431671","431671"],"URL":"https:\/\/doi.org\/10.1155\/2014\/431671","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}