Predator-taxis creates spatial pattern of a predator-prey model

In this paper, we investigate the spatial pattern formation to a predator-prey model with the predator-taxis under the homogeneous zero -flux boundary conditions. Firstly, we employ the predator-taxis coefficient as the potential critical value of the Turing bifurcation to perform its role in forming the spatial pattern. One finds that there are multiple thresholds of the Turing bifurcation. Hereafter, we focus on the direction of the Turing bi-furcation. To this end, the technique of the weakly nonlinear analysis is employed to deduce the amplitude equa-tion near the threshold of the Turing bifurcation in one-dimensional space. It is found that the predator-taxis can create the subcritical or the supercritical Turing bifurcation. Finally, numerical experiments check the theoretical analysis well and obtain the spatial patterns with the different predator-taxis coefficients.(c) 2022 Elsevier Ltd. All rights reserved.