Sharp oscillatory traveling waves of structured population dynamics model with degenerate diffusion

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Xu, Tianyuan^1,4  Ji, Shanming^2,4  Mei, Ming^3,4  Yin, Jingxue¹ 

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Guangdong, Peoples R China

[2] South China Univ Technol, Sch Math, Guangzhou 510641, Guangdong, Peoples R China

[3] Champlain Coll St Lambert, Dept Math, St Lambert, PQ J4P 3P2, Canada

[4] McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada

关键词: Traveling waves;    Time delay;    Degenerate diffusion;    Oscillatory waves;    Sharp waves;   

DOI  :  10.1016/j.jde.2020.06.029

来源: Elsevier

【 摘 要 】

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. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free