一类带年龄结构周期型反应扩散种群系统的空间动力学

Spatial Dynamics on a Periodic Reaction-diffusion Population Model with Age-structure

研究了一类带年龄结构和扩散项的周期生物种群模型，通过对相应时滞微分系统的空间动力学讨论，证明其存在全局渐近稳定的正周期解．并利用单调周期半流理论，研究了反应扩散生物系统周期行波解和渐近波速c＊的存在性，即：c〉c＊时系统存在周期行波解，c〈c＊时不存在连续的周期行波解．

A class of periodic reaction-diffusion population model with age-structure and dispersal kernel is discussed in the paper. Via study on the spatial dynamics to the relative delay differential equations, we prove the the system admits an unique positive periodic so- lution, which is also globally asymptotically stable. By appealing to the theory of monotonic periodic semiflows, we establish the traveling wave solution and spreading speed c＊ with the periodic reaction-diffusion population model. That is, continuous periodic traveling wave exists when wave speed c 〉 c＊, and nonsexists when c 〈 c＊.