中文摘要：

考虑一类带负交叉扩散项二维系统的Turing斑图生成及其选择问题.先利用稳定性理论和Hopf分支理论得到Turing斑图的存在区域,再利用多重尺度分析法推导系统的振幅方程,并给出Turing斑图的选择结果.最后考虑一个具有比率依赖的Holling-Tanner捕食模型生态系统,利用MATLAB软件对该模型的斑图生成及选择结果进行数值模拟,得到了包括点状、条状以及二者共存等不同类型的Turing斑图.

英文摘要：

We considered the generation and selection of Turing pattern of a class of two dimensional system with negative cross-diffusion. Firstly, the existence region of Turing pattern was obtained by using stability theory and Hopf bifurcation theory. Secondly, the amplitude equations of the system were derived by using multi-scales analysis method, and the selection result of Turing pattern was given. Finally, we considered a specific ecosystem with a ratio dependent Holling-Tanner predator- prey model. MATLAB software was used to simulate the pattern generation and selection results of the model, and the different types of Turing patterns, such as dot, strip and the coexistence of the two types were obtained.