This paper is devoted to the study of propagation dynamics for a time periodic nonlocal dispersal model with stage structure. In the case where the birth rate function is monotone, we establish the existence of the spreading speed and its coincidence with the minimal wave speed for monotone periodic traveling waves by appealing to the theory developed for monotone semiflows. In the case where the birth rate function is non-monotone, we first obtain the spreading properties by the squeezing technique combined with some known results for the monotone case, and then investigate the existence of periodic traveling waves by using the asymptotic fixed point theorem due to the lack of parabolic estimates and compactness. Finally, we apply the general results to the Nicholson’s blowflies model for its spatial dynamics.

中文翻译：

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具有阶段结构的时间周期非局部扩散模型中的传播动力学

本文致力于具有阶段结构的时间周期非局部扩散模型的传播动力学研究。在出生率函数为单调的情况下，我们通过为单调半流开发的理论，建立了扩展速度的存在及其与单调周期性行波的最小波速的一致。在出生率函数为非单调的情况下，我们首先通过压缩技术结合单调情况的一些已知结果来获得扩展特性，然后通过使用渐近不动点定理来研究周期行波的存在性缺乏抛物线估计和紧凑性。最后，我们将一般结果应用于Nicholson的s蝇模型的空间动力学。