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The aim of this paper is to establish a precise illustration for the structure of the nonconstant steady states for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis. We treat the nonlinear prey‐taxis as a bifurcation parameter to analyze the bifurcation structure of the system. Furthermore, the exported global bifurcation theorem, under a rather natural condition, offers the existence of nonconstant steady states. In the proof, a priori estimates of steady states will play an important role. The local stability analysis with a numerical simulation and bifurcation analysis are given. Finally, some conclusions including biological meanings are performed to summarize our main analytic results and future investigations. [ABSTRACT FROM AUTHOR]

In this paper, we consider the time‐dependent Stokes problem in a three‐dimensional domain with mixed boundary conditions. The discretization relies on spectral methods with respect to the space variables and Euler's implicit scheme with respect to the time variable, then by the second order BDF method. A detailed numerical analysis leads to a priori error estimates for each numerical scheme. [ABSTRACT FROM AUTHOR]