Global dynamics of evolution systems with asymptotic annihilation

Taishan Yi; Xiao-Qiang Zhao

doi:10.3934/dcds.2023025

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2023, Volume 43, Issue 7: 2693-2720. Doi: 10.3934/dcds.2023025

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Global dynamics of evolution systems with asymptotic annihilation

Taishan Yi^1, and
Xiao-Qiang Zhao^2, ,

1.
School of Mathematics (Zhuhai), Sun Yat-Sen University, Zhuhai, Guangdong, China
2.
Department of Mathematics and Statistics, Memorial University of Newfoundland, Canada

^*Corresponding author: Xiao-Qiang Zhao
^*Corresponding author: Xiao-Qiang Zhao

Received: December 2022

Early access: March 2023

Published: July 2023

T. Yi's research is supported by NSFC (NO.11971494, 12231008), and X.-Q. Zhao's research is supported in part by the NSERC of Canada (RGPIN-2019-05648).

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Abstract

This paper is devoted to the research on the global dynamics for a large class of evolution systems with uniform asymptotic annihilation. We first introduce the concept of the asymptotic spectral radius and study the associated principal eigenvalue problem. Then we establish the asymptotic annihilation and the threshold dynamics for such systems. Finally we apply the developed theory to investigate the global attractivity of a positive fixed point for an integro-difference equation and the propagation phenomenon for cooperative reaction-diffusion systems with a shifting habitat.

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Mathematics Subject Classification: Primary: 35B40, 35C07, 37C65; Secondary: 92D25.

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