中文摘要：

通过研究含有Lotka-Volterra捕食和被捕食动力学行为的反应扩散方程的交叉扩散项来解释斑图的形成机制.借此来说明能导致部分斑图出现的交叉耗散项在失稳机制中的重要性.在稳定区域的附近采用弱非线性分析方法来研究斑图的振幅,得到其Stuart-Landau规范型振幅方程.最后,当斑图作为行波的波前侵入区域时,可以得到Ginzburg-Landau规范型振幅方程,这一方程常常用来研究波的形状和波速.

英文摘要：

The pattern formation system was explained by studying the cross-diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics.It was indicated that the cross-diffusion term that leads to the emergence of spatial patterns is responsible of the destabilizing mechanism.The amplitude of patterns were studied by weakly nonlinear analysis near marginal stability,and the Stuart-Landau amplitude equation was obtained.Finally,when the patterns invaded the domain as a travelling wavefront,the Ginzburg-Landau amplitude equation which was able to describe the shape and speed of the wave was derived.