{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:07Z","timestamp":1740134527267,"version":"3.37.3"},"reference-count":12,"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 ratio-dependent predator-prey model incorporating a prey refuge with disease in the prey population is formulated and analyzed. The effects of time delay due to the gestation of the predator and stage structure for the predator on the dynamics of the system are concerned. By analyzing the corresponding characteristic equations, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the system is discussed, respectively. Further, it is proved that the system undergoes a Hopf bifurcation at the coexistence equilibrium, when<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>\u03c4<\/mml:mi><mml:mo>=<\/mml:mo><mml:msub><mml:mrow><mml:mi>\u03c4<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math>. By comparison arguments, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium. By using an iteration technique, sufficient conditions are derived for the global attractivity of the coexistence equilibrium of the proposed system.<\/jats:p>","DOI":"10.1155\/2014\/978758","type":"journal-article","created":{"date-parts":[[2014,3,23]],"date-time":"2014-03-23T21:04:04Z","timestamp":1395608644000},"page":"1-10","source":"Crossref","is-referenced-by-count":1,"title":["Stability Analysis of a Ratio-Dependent Predator-Prey Model Incorporating a Prey Refuge"],"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"}]},{"given":"Guanghui","family":"Feng","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China"}]}],"member":"311","reference":[{"key":"6","doi-asserted-by":"crossref","first-page":"700","DOI":"10.1098\/rspa.1927.0118","volume":"115","year":"1927","journal-title":"Proceedings of the Royal Society A"},{"year":"1991","key":"2"},{"issue":"4","key":"9","doi-asserted-by":"crossref","first-page":"473","DOI":"10.15388\/NA.15.4.14319","volume":"15","year":"2010","journal-title":"Nonlinear Analysis: Modelling and Control"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(01)00156-4"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(97)00056-4"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1007\/s10114-002-0234-2"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2007.03.015"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2007.01.019"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/0025-5564(90)90019-U"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139993252839"},{"year":"1977","key":"3"},{"volume":"191","year":"1993","key":"7"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/978758.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/978758.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/978758.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,16]],"date-time":"2020-08-16T18:16:03Z","timestamp":1597601763000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/978758\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":12,"alternative-id":["978758","978758"],"URL":"https:\/\/doi.org\/10.1155\/2014\/978758","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}