Yin, Hongwei; Xiao, Xiaoyong; Wen, Xiaoqing Turing patterns in a predator-prey system with self-diffusion. (English) Zbl 1420.92101 Abstr. Appl. Anal. 2013, Article ID 891738, 10 p. (2013). Summary: For a predator-prey system, cross-diffusion has been confirmed to emerge Turing patterns. However, in the real world, the tendency for prey and predators moving along the direction of lower density of their own species, called self-diffusion, should be considered. For this, we investigate Turing instability for a predator-prey system with nonlinear diffusion terms including the normal diffusion, cross-diffusion, and self-diffusion. A sufficient condition of Turing instability for this system is obtained by analyzing the linear stability of spatial homogeneous equilibrium state of this model. A series of numerical simulations reveal Turing parameter regions of the interaction of diffusion parameters. 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