{"title":"Spreading dynamics of a discrete Nicholson's blowflies equation with distributed delay","authors":"Ruiwen Wu, Zhaoquan Xu","doi":"10.1017/prm.2023.34","DOIUrl":null,"url":null,"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.","PeriodicalId":54560,"journal":{"name":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","volume":"20 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of Edinburgh Section A-Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/prm.2023.34","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.