Abstract We consider a population dynamics model with degenerate diffusion and time delay. We discover sharp-oscillatory waves with sharp edges and non-decaying oscillations arising from density-dependent dispersal and reproduction with age structure. Degenerate diffusion and bad effect of time delay prevent the use of existing approaches. Here, we develop a new delayed iteration framework to show the existence of these peculiar waves. In particular, the estimate of the admissible wave speed is highly nontrivial. We employ a new phase transform method coupled with the detailed analysis of phase energy. Furthermore, we give a complete characterization of the dynamical behaviors of various kinds of waves. Our results indicate that simple invasion rules can generate complex wave patterns and provide some interesting insights into the ecological dynamics.

中文翻译：

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具有简并扩散的结构化种群动力学模型的尖锐振荡行波

摘要 我们考虑具有退化扩散和时间延迟的种群动态模型。我们发现了具有尖锐边缘的尖锐振荡波和由年龄结构的密度依赖性扩散和繁殖引起的非衰减振荡。退化扩散和时间延迟的不良影响阻碍了现有方法的使用。在这里，我们开发了一个新的延迟迭代框架来展示这些奇特波的存在。特别是，可容许波速的估计非常重要。我们采用了一种新的相位变换方法，并结合了对相位能量的详细分析。此外，我们给出了各种波的动力学行为的完整表征。