Local Stability of Traveling Wavefronts for a “Food-Limited” Population Model with Spatio-Temporal Delay

本文主要研究了一类具有时空时滞的“食物有限”种群模型的波前解的稳定性。利用线性化算子的谱分析，证明了波前解在有界一致连续函数空间中是不稳定的。但是，当波前解的初始扰动属于某个指数加权函数空间时，波前解是渐近稳定的。This paper is concerned with the stability of traveling wavefronts for a “food-limited” population model with spatio-temporal delay. By the spectral analysis of the linearized operators, we show that the traveling wavefronts are essentially unstable in the space of bounded and uniformly continuous functions. However, if the initial perturbations of the traveling wavefronts belong to certain exponential weighted spaces, then we prove that the traveling wavefronts are asymptotically stable in the exponential weighted spaces.