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(9 citation statements)

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“…Replacing (M 1 , M 2 , M 3 ) and (δ 1 , δ 2 , δ 3 ) by ū (1) ,v (1) ,w (1) and u (1) , v (1) , w (1) in the same iteration process (3.12), the second iterations ū (2) ,v (2) ,w (2) and u (2) , v (2) , w (2) are also constants and are given by (3.12) with k = 2. A continuation of the above iteration process leads to the constant sequences ū (k) ,v (k) ,w (k) , u (k) , v (k) , w (k) for every k. By Theorem 2.1, the constant limits…”

confidence: 98%

“…Replacing (M 1 , M 2 , M 3 ) and (δ 1 , δ 2 , δ 3 ) by ū (1) ,v (1) ,w (1) and u (1) , v (1) , w (1) in the same iteration process (3.12), the second iterations ū (2) ,v (2) ,w (2) and u (2) , v (2) , w (2) are also constants and are given by (3.12) with k = 2. A continuation of the above iteration process leads to the constant sequences ū (k) ,v (k) ,w (k) , u (k) , v (k) , w (k) for every k. By Theorem 2.1, the constant limits…”

confidence: 98%

“…In recent years, attention has been given to one-prey two-predator systems with various types of reaction functions, including ratio-dependent functional response (cf. [2,7,8,[12][13][14]25]). However, most of the discussions are either for semilinear reaction diffusion systems or for ordinary differential systems with either the traditional Lotka-Volterra type of reaction functions or ratio-dependent reaction functions (cf.…”

confidence: 97%

“…For example, Sarwardi et al [27] focused on the local and the global stability and the bifurcations of a competitive preypredator system with a prey refuge, Ko and Ahn [16] discussed the global attractor, persistence and the stability of all non-negative equilibria of a diffusive one-prey and two-competing-predator system with a ratio-dependent functional response, Pan et al [25] considered Gause , s principle in interspecific competition of the cyclic predatorprey system, Qun Liu et al [23] addressed the global stability of a stochastic predatorprey system with infinite delays. For more related works on this topic, one can see [2,3,6,[9][10][11][12]14,15,18,20,24,26,28,29,31,34,35,38]. In 2001, Zhang et al [36] investigated the permanence of the following non-autonomous competing model dx 1 (t)…”

confidence: 99%

“…In particular, there have been extensive results on existence of almost periodic solutions of differential equations in the literatures (see [1,8,17,19,33]). The main object of this paper is to investigate the almost periodic solutions of model (2). By the analysis on the almost periodic solutions of model (2), we can find the coexistence conditions of two competing populations, which can help human beings to control ecological balance.…”

confidence: 99%

“…Pang and Wang [11] study a class of two-predator-one-prey ecosystem and show that the unique positive equilibrium solution of the system is globally asymptotically stable. Baek et al [12] study a x 1 (t) elliptic system with ratio-dependent functional responses. By employing a comparison argument for the elliptic problem and the fixed-point theory applied to a positive cone on a Banach space, authors examine the positive coexistence of one prey and two competing predators in an interacting system with ratio-dependent functional responses under a hostile environment.…”

confidence: 99%