Spreading dynamics of a discrete Nicholson's blowflies equation with distributed delay

Ruiwen Wu, Zhaoquan Xu
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引用次数: 3

Abstract

This paper is focused on spreading dynamics for a discrete Nicholson's blowflies model with time convolution kernel. This problem arises in the invasive activity of blowflies scattered in discrete spatial environment and has distributed maturated age. We found that for a general convolution kernel, the model can exhibit travelling wave phenomena in a discrete spatial habitat. In particular, we determine the minimal wave speed of travelling waves by deriving the non-existence of travelling waves, and we demonstrate that the minimal wave speed can determine the long time behaviour of solutions with compact initial function. Moreover, we prove that all travelling waves are strictly increasing, which implies that the waveforms remain monotone in the propagation process. Some numerical simulations are also presented to confirm the analytical results.
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具有分布延迟的离散尼克尔森方程的扩展动力学
研究了具有时间卷积核的离散尼克尔森飞蝇模型的扩散动力学问题。这一问题出现在散在离散空间环境中的苍蝇的入侵活动中,并且成熟年龄分布。我们发现,对于一般卷积核,该模型可以在离散的空间生境中表现出行波现象。特别地,我们通过推导行波的不存在性来确定行波的最小波速,并证明了最小波速可以决定初始函数紧凑的解的长时间行为。此外,我们证明了所有的行波都是严格递增的,这意味着波形在传播过程中保持单调。通过数值模拟验证了分析结果。
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来源期刊
CiteScore
3.00
自引率
0.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: A flagship publication of The Royal Society of Edinburgh, Proceedings A is a prestigious, general mathematics journal publishing peer-reviewed papers of international standard across the whole spectrum of mathematics, but with the emphasis on applied analysis and differential equations. An international journal, publishing six issues per year, Proceedings A has been publishing the highest-quality mathematical research since 1884. Recent issues have included a wealth of key contributors and considered research papers.
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