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Spatio-temporal dynamics of a lattice prey–predator system with non-local diffusion in a periodic habitat

Part of: Parabolic equations and systems Representations of solutions

Published online by Cambridge University Press:  31 March 2025

Wan-Tong Li ,
Ming-Zhen Xin  and
Xiao-Qiang Zhao
Wan-Tong Li
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, People’s Republic of China
Ming-Zhen Xin*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, People’s Republic of China Department of Mathematics and Statistics, Memorial University of Newfoundland, A1C 5S7 St. John’s, NL, Canada ([email protected]) (corresponding author)
Xiao-Qiang Zhao
Affiliation:
Department of Mathematics and Statistics, Memorial University of Newfoundland, A1C 5S7 St. John’s, NL, Canada
*
*Corresponding author.
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Abstract

This article is concerned with the spreading speed and traveling waves of a lattice prey–predator system with non-local diffusion in a periodic habitat. With the help of an associated scalar lattice equation, we derive the invasion speed for the predator. More specifically, when the dispersal kernel of the predator is exponentially bounded, the invasion speed is finite and can be characterized in terms of principal eigenvalues; while the dispersal kernel is algebraically decaying, the invasion speed is infinite and the accelerated spreading rate is obtained. Furthermore, the existence and non-existence of traveling waves connecting the semi-equilibrium point to a uniformly persistent state are established.

Keywords

accelerated propagationlattice prey–predator systemsperiodic habitatsspreading speedstraveling waves

MSC classification

Primary: 35C07: Traveling wave solutions
Secondary: 35K57: Reaction-diffusion equations 92D25: Population dynamics (general)
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , First View , pp. 1 - 43
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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