Geodesic
Permanence of predator-prey system with infinite delay
Electronic journal of differential equations, Tome 2004 (2004)
In this paper we consider a predator-prey system with periodic coefficients and infinite delay, in which the prey has a history that takes them through two stages, immature and mature. We provide a sufficient and necessary condition to guarantee the permanence of the system. The system has a positive periodic solution under this condition. Some known results are extended to the delay case.
Classification : 92D25, 34C25
Keywords: predator-prey system, stage structure, permanence, periodic solution, infinite delay 
@article{EJDE_2004__2004__a2,
     author = {Sun,  Jingan and Cui,  Yonghong},
     title = {Permanence of predator-prey system with infinite delay},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1056.92050},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a2/}
}
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%A Cui,  Yonghong
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Sun,  Jingan; Cui,  Yonghong. Permanence of predator-prey system with infinite delay. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a2/