Recent developments on a singular predator-prey model

Yu-Shuo Chen; Jong-Shenq Guo; Masahiko Shimojo

doi:10.3934/dcdsb.2020040

Article Contents

2021, Volume 26, Issue 4: 1811-1825. Doi: 10.3934/dcdsb.2020040

This issue Previous Article Traveling wave solutions of a free boundary problem with latent heat effect Next Article Traveling waves in quadratic autocatalytic systems with complexing agent

Recent developments on a singular predator-prey model

1.
Department of Mathematics, Tamkang University, Tamsui, New Taipei City 25137, Taiwan
2.
Department of Applied Mathematics, Okayama University of Science, Okayama 700-0005, Japan

^* Corresponding author: Jong-Sheng Guo
^* Corresponding author: Jong-Sheng Guo

Received: May 2019

Early access: February 2020

Published: April 2021

This work is partially supported by the Ministry of Science and Technology of Taiwan under the grants 106-2811-M-032-008 and 105-2115-M-032-003-MY3.

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Abstract

This work is concerned with the dynamical behaviors of a singular predator-prey model. We first review some well-known results obtained recently. Then we give some new results on the spreading speed of the predator, the existence vs non-existence of traveling waves connecting the predator-free state to the co-existence state, and the existence vs non-existence of spatially periodic traveling waves to this singular predator-prey system.

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Mathematics Subject Classification: Primary: 35K55, 35K57; Secondary: 92D25, 92D40.

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References

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