具有非线性收获效应的捕食者-食饵系统的空间Turing斑图

摘要 研究了一类带有非线性食饵收获效应的捕食者-食饵系统的Turing斑图的生成及选择问题.首先利用稳定性理论给出了由交叉扩散项引起的Turing不稳定条件和分支理论分析得到了系统Turing斑图的存在区域，然后运用多重尺度分析法推导了系统的振幅方程，给出了Turing斑图的选择结果.最后利用Matlab软件对系统Turing斑图的生成和选择结果进行了数值模拟.结果展示了系统有丰富的Turing斑图，如点状、条状以及二者共存.
Abstract：We study the formation and selection of Turing patterns for a class of predator-prey systems with nonlinear harvesting effect. Firstly, the conditions of Turing instability induced by cross-diffusion terms are given by stability theory, and the existence region of Turing patterns of the system are obtained by bifurcation theory. Secondly, the amplitude equations of the system are derived using the multi-scales analysis method, and the selection results of Turing patterns are given. Finally, Matlab is used to simulate the pattern formation and selection results of the system. The results show that the system has rich Turing patterns, such as spot, stripe, and coexistence of the two types.