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Xiaoli Wang Wendi Wang Guohong Zhang 《Mathematical Methods in the Applied Sciences》2015,38(3):431-443
We study pattern formations in a predator–prey model with prey‐taxis. It is proved that a branch of nonconstant solutions can bifurcate from the positive equilibrium only when the chemotactic is repulsive. Furthermore, we find the stable bifurcating solutions near the bifurcation point under suitable conditions. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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A reaction‐diffusion two‐predator‐one‐prey system with prey‐taxis describes the spatial interaction and random movement of predator and prey species, as well as the spatial movement of predators pursuing preys. The global existence and boundedness of solutions of the system in bounded domains of arbitrary spatial dimension and any small prey‐taxis sensitivity coefficient are investigated by the semigroup theory. The spatial pattern formation induced by the prey‐taxis is characterized by the Turing type linear instability of homogeneous state; it is shown that prey‐taxis can both compress and prompt the spatial patterns produced through diffusion‐induced instability in two‐predator‐one‐prey systems. 相似文献
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邵建峰 《数学的实践与认识》2001,31(3):273-277
本文讨论了二维平面上给定区域内的凸多边形切割问题 .按“顶点度数”该问题可以分为两种类型 .在两种类型下并给出了凸多边形的简单切割方法 . 相似文献
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《Mathematical Methods in the Applied Sciences》2018,41(10):3570-3587
In this paper, we consider a generalized predator‐prey system with prey‐taxis under the Neumann boundary condition. We investigate the local and global asymptotical stability of constant steady states (including trivial, semitrivial, and interior constant steady states). On the basis of a priori estimate and the fixed‐point index theory, several sufficient conditions for the nonexistence/existence of nonconstant positive solutions are given. 相似文献
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