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A predator–prey system with two impulses on the diseased prey and a Beddington–DeAngelis response
Author(s) -
Wang Xia,
Song Xinyu
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1169
Subject(s) - predation , floquet theory , mathematics , functional response , stability (learning theory) , predator , control theory (sociology) , comparison theorem , differential equation , partial differential equation , mathematical optimization , mathematical analysis , ecology , biology , computer science , artificial intelligence , physics , nonlinear system , control (management) , quantum mechanics , machine learning
A predator–prey system with two impulses on the diseased prey is formulated and analyzed for the purpose of integrated pest management. The local and global stability of the susceptible pest‐eradication periodic solution, as well as the permanence of the system, are obtained under the sufficient conditions by means of Floquet's theory for impulsive differential equations. Finally, we interpret our mathematical results. Copyright © 2009 John Wiley & Sons, Ltd.