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

Part of: Miscellaneous topics - Partial differential equations General theory in ordinary differential equations

Published online by Cambridge University Press:  12 May 2023

Ruiwen Wu  and
Zhaoquan Xu
Ruiwen Wu
Affiliation:
Department of Mathematics, Jinan University, Guangzhou 510632, China (ruiwenwu@jnu.edu.cn; xuzhqmaths@126.com)
Zhaoquan Xu
Affiliation:
Department of Mathematics, Jinan University, Guangzhou 510632, China (ruiwenwu@jnu.edu.cn; xuzhqmaths@126.com)
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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.

Keywords

minimal wave speedspreading speedtravelling wavesmonotonicityNicholson's blowflies model

MSC classification

Primary: 34A33: Lattice differential equations
Secondary: 35R10: Partial functional-differential equations 92D25: Population dynamics (general)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 23
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Copyright
Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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