中文摘要：

本文讨论一类体积填充趋化模型（＊）的不稳定常数平衡解附近的非线性动力学性态.研究表明{Ut=（d1U-χU（1-U/γ）V）,（＊）Vt=d22V＋U-V,对任意给定的一般初始扰动δ,在以lnδ-1为阶的时间段内,该扰动的非线性演化由相应的线性化系统的最快增长模式所控制,并对斑图生成进行定量的刻画.

英文摘要：

In this paper, we deal with the Neumann initial-boundary value problem in a d-dimen- sional box T^d=（0,π）^d（ = 1,2,3） for a volume-filling chemotaxis system {Ut=（d1U-χU（1-U/γ）V）,（＊）Vt=d22V＋U-V. Nonlinear dynamics near an unstable constant equilibrium in （＊） is considered. It is proved that for any given general perturbation of magnitude δ, linear fastest growing modes determine the nonlinear evolution for the model （＊） over a time period of the order In δ-1. Our result provides a rigorous mathematical description for the pattern formation in the model （＊）.