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Vietnam Journal of Mathematics 39:1 (2011) 105-123 

On the Asymptotic Behavior of Solutions and Positive Almost Periodic Solution

for Predator-Prey System with the Holling Type II Functional Response

Trinh Tuan Anh and Tong Thanh Trung

 

Abstract. In this paper, we investigate a predator-prey population which is modeled by a system of dierential equations modified Leslie-Gower and Holling type II schemes with time-dependent parameters. We establish a sucient condition posed on the behavior at infinity of coecients for globally asymptotic stability of solutions. The existence and uniqueness of positive bounded solution of system are also proved. In the case where the coecients of equations are almost periodic functions, it is showed that there exists a unique positive almost periodic solution which attracts every solution starting in .

.

2000 Mathematics Subject Classification: 92D25, 93A30, 93D99.

Keywords: Predator-prey system; Globally asymptotically stable; Positive bounded solution; Periodic solu-tion; Almost periodic solution, Functional response.

 

 

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