Permanence and global asymptotical stability of a predator–prey model with mutual interference

In this paper, a predator-prey system with mutual interference is studied. Some sufficient conditions are obtained for permanence and global asymptotical stability of the system by using the comparison theorem and constructing a suitable Lyapunov function. It is significant that the mutual interference mm, in Theorem 4.1 and Theorem 4.2, is allowed to be any real-valued number in interval (0, 1), which improves the corresponding results in Wang and Zhu (2008) [14], Wang (2009) [13], Lin and Chen (2009) [16] and Wang, Du and Liang (2010) [17] (where the mutual constant mm needs to be a rational number). Moreover, it solves the open problem posed by Lin in [16].