中文摘要：

应用嵌入定理，能量估计方法和bootstrp技巧，讨论一类非线性信号动力学趋化模型的不稳定正常数平衡解附近的非线性动力学性态．对正常数平衡解失稳初期时空斑图的非线性演化给出严格的定量刻画．

英文摘要：

Using the embedding theorem, the energy estimates and bootstrap arguments, nonlinear dynamics near an unstable constant equilibrium in the nonlinear signal kinetics chemotaxis model is discussed. Our results indeed provide a rigorous mathematical description for the nonlinear evolution of early spatiotemporal pattern formation on the unstable positive constant equilibrium.