{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:14:24Z","timestamp":1753881264645,"version":"3.41.2"},"reference-count":26,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,8,14]],"date-time":"2012-08-14T00:00:00Z","timestamp":1344902400000},"content-version":"vor","delay-in-days":226,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Chonqqing Natural Science Foundation","award":["2008BB0009"],"award-info":[{"award-number":["2008BB0009"]}]},{"name":"Ministry of Personnel of China","award":["2008BB0009"],"award-info":[{"award-number":["2008BB0009"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>A general predator\u2010prey system is studied in a scheme where there is periodic impulsive perturbations. This scheme has the potential to protect the predator from extinction but under some conditions may also serve to lead to extinction of the prey. Conditions for extinction and permanence are obtained via the comparison methods involving monotone theory of impulsive systems and multiple Liapunov functions, which establish explicit bounds on solutions. The existence of a positive periodic solution is also studied by the bifurcation theory. Application is given to a Lotka\u2010Volterra predator\u2010prey system with periodic impulsive immigration of the predator. It is shown that the results are quite different from the corresponding system without impulsive immigration, where extinction of the prey can never be achieved. The prey will be extinct or permanent independent of whether the system without impulsive effect immigration is permanent or not. The model and its results suggest an approach of pest control which proves more effective than the classical one.<\/jats:p>","DOI":"10.1155\/2012\/521729","type":"journal-article","created":{"date-parts":[[2012,8,14]],"date-time":"2012-08-14T21:00:50Z","timestamp":1344978050000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Extinction and Permanence of a General Predator\u2010Prey System with Impulsive Perturbations"],"prefix":"10.1155","volume":"2012","author":[{"given":"Xianning","family":"Liu","sequence":"first","affiliation":[]},{"given":"Lansun","family":"Chen","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,8,14]]},"reference":[{"volume-title":"Impulsive Differential Equations: Periodic Solutions and Applications","year":"1993","author":"Bainov D. 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