{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T02:08:18Z","timestamp":1740103698571,"version":"3.37.3"},"reference-count":46,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,4,17]],"date-time":"2020-04-17T00:00:00Z","timestamp":1587081600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11371230","S2015SF002","SDKDYC190351","2014TDJH102"],"award-info":[{"award-number":["11371230","S2015SF002","SDKDYC190351","2014TDJH102"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007129","name":"Natural Science Foundation of Shandong Province","doi-asserted-by":"publisher","award":["11371230","S2015SF002","SDKDYC190351","2014TDJH102"],"award-info":[{"award-number":["11371230","S2015SF002","SDKDYC190351","2014TDJH102"]}],"id":[{"id":"10.13039\/501100007129","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004295","name":"Shandong University of Science and Technology","doi-asserted-by":"publisher","award":["11371230","S2015SF002","SDKDYC190351","2014TDJH102"],"award-info":[{"award-number":["11371230","S2015SF002","SDKDYC190351","2014TDJH102"]}],"id":[{"id":"10.13039\/501100004295","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004295","name":"Shandong University of Science and Technology","doi-asserted-by":"publisher","award":["11371230","S2015SF002","SDKDYC190351","2014TDJH102"],"award-info":[{"award-number":["11371230","S2015SF002","SDKDYC190351","2014TDJH102"]}],"id":[{"id":"10.13039\/501100004295","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Joint Innovative Center for Safe and Effective Mining Technology and Equipment of Coal Resources, Shandong Province of China","award":["11371230","S2015SF002","SDKDYC190351","2014TDJH102"],"award-info":[{"award-number":["11371230","S2015SF002","SDKDYC190351","2014TDJH102"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,4,17]]},"abstract":"<jats:p>An integrated pest management prey-predator model with ratio-dependent and impulsive feedback control is investigated in this paper. Firstly, we determine the Poincar\u00e9 map which is defined on the phase set and discuss its main properties including monotonicity, continuity, and discontinuity. Secondly, the existence and stability of the boundary order-one periodic solution are proved by the method of Poincar\u00e9 map. According to the Poincar\u00e9 map and related differential equation theory, the conditions of the existence and global stability of the order-one periodic solution are obtained when<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>\u03a6<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:msub><mml:mrow><mml:mi>y<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:mfenced><mml:mo>&lt;<\/mml:mo><mml:msub><mml:mrow><mml:mi>y<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>, and we prove the sufficient and necessary conditions for the global asymptotic stability of the order-one periodic solution when<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>\u03a6<\/mml:mi><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:msub><mml:mrow><mml:mi>y<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:mfenced><mml:mo>&gt;<\/mml:mo><mml:msub><mml:mrow><mml:mi>y<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>. Furthermore, we prove the existence of the order-<jats:italic>k<\/jats:italic><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mfenced open=\"(\" close=\")\" separators=\"|\"><mml:mrow><mml:mi>k<\/mml:mi><mml:mo>\u2265<\/mml:mo><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:mrow><\/mml:math>periodic solution under certain conditions. Finally, we verify the main results by numerical simulation.<\/jats:p>","DOI":"10.1155\/2020\/2376374","type":"journal-article","created":{"date-parts":[[2020,4,17]],"date-time":"2020-04-17T23:30:24Z","timestamp":1587166224000},"page":"1-12","source":"Crossref","is-referenced-by-count":1,"title":["Poincar\u00e9 Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model"],"prefix":"10.1155","volume":"2020","author":[{"given":"Zhenzhen","family":"Shi","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Shandong University of Science and Technology, Qingdao 266590, Shandong, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingjian","family":"Li","sequence":"additional","affiliation":[{"name":"College of Foreign Languages, Shandong University of Science and Technology, Qingdao 266590, Shandong, 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