permanence and global asymptotic stability of a delayed predator-prey model with hassell-varley type functional response
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abstract
here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.
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Tianwei Zhang 1,*, Liyan Pang 2 and Yongzhi Liao 3 1 City College, Kunming University of Science and Technology, Kunming 650051, China 2 School of Mathematics and Computer Science, Ningxia Normal University, Guyuan, Ningxia 756000, China; [email protected] 3 School of Mathematics and Computer Science, Panzhihua University, Panzhihua, Sichuan 617000, China; [email protected] * Correspondence: zh...
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Predator-prey models with Hassell-Varley type functional response are appropriate for interactions where predators form groups and have applications in biological control. Here we present a systematic global qualitative analysis to a general predator-prey model with Hassell-Varley type functional response. We show that the predator free equilibrium is a global attractor only when the predator d...
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Recently, there were many works on predator-prey system done by scholars [1–6]. In particular, since Hassell-Varley [7] proposed a general predator-prey model with Hassell-Varley type functional response in 1969, many excellent works have been conducted for the Hassell-Varley type system [1, 7–13]. Liu and Huang [8] studied the following discrete predator-prey system with Hassell-Varley-Holling...
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Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 37
issue No. 3 2011
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