In this paper, a predator-prey model with mixed-type functional response is investigated. Sufficient conditions are derived that guarantee the permanence of the system. Meanwhile, when the system is periodic, we obtain the sufficient conditions which guarantee the existence, uniqueness and global asymptotic stability of the positive periodic solution. Numerical simulations are also presented to...

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results. Copyright q 2008 Can-Yun Huang et al. This is an open acce...

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...

TIn this paper, the existence of periodic solutions of a predator-prey model with Beddington-DeAngelis type functional response is investigated by using the Gaines and Mawhins continuation theorem of coincidence degree theory on time scales. Some conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the con...

In this paper, a prey-predator model with a social activity of prey population has been analyzed. In some ecological situations, the prey-predator interaction occurs only at the outer surface of a herd formed by prey population. To model this phenomenon, the square root of prey density has been used in the functional response. The basic model is formulated with this modified functional response...

where u and v, respectively, represent the populations of the prey and the predator, and r, s, K, h are positive constants. The prey grows logistically with carrying capacity K and intrinsic growth rate r in the absence of predation. The predator consumes the prey according to the functional response f(u) and grows logistically with intrinsic growth rate s. The carrying capacity of the predator...

We study a diffusive predator-prey system with a ratio-dependent functional response when a prey population is infected under homogeneous Neumann boundary condition. All non-negative and positive equilibria are investigated, and the conditions that give rise to asymptotic behavior of these equilibria are examined. In particular, we present a biological interpretation of disease-free and total e...

It is known that one of important factors impacted on a predator-prey system is the functional response. Holling proposed three types of functional response functions, namely, Holling I, Holling II, and Holling III, which are all monotonously nondescending 1 . But for some predator-prey systems, when the prey density reaches a high level, the growth of predator may be inhibited; that is, to say...

Ecological systems are mainly characterized by the interaction between species and their surrounding natural environment 1 . Especially, the dynamic relationship between predators and their preys has long been and will continue to be one of the dominant themes in both ecology and mathematical ecology, due to its universal existence and importance 2– 4 . The interaction mechanism of predators an...

and Applied Analysis 3 Proposition 2.2. Let x1 t , x2 t be any positive solution of system 1.1 , then lim n→ ∞ supxi n ≤ Mi, i 1, 2, 2.3