Asymptotic spreading for a time-periodic predator-prey system

Xinjian Wang; Guo Lin

doi:10.3934/cpaa.2019133

Article Contents

2019, Volume 18, Issue 6: 2983-2999. Doi: 10.3934/cpaa.2019133

This issue Previous Article Existence results of solitary wave solutions for a delayed Camassa-Holm-KP equation Next Article $ L^{p, q} $ estimates on the transport density

Asymptotic spreading for a time-periodic predator-prey system

Xinjian Wang and
Guo Lin^,

Key Laboratory of Applied Mathematics and Complex Systems, School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China

^* Corresponding author
^* Corresponding author

Received: June 30, 2018

Revised: December 31, 2018

Published: May 2019

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Abstract

This paper is concerned with asymptotic spreading for a time-periodic predator-prey system where both species synchronously invade a new habitat. Under two different conditions, we show the bounds of spreading speeds of the predator and the prey, which is proved by the theory of asymptotic spreading of scalar equations, comparison principle and generalized eigenvalue. We show either the predator or the prey has a spreading speed that is determined by the linearized equation at the trivial steady state while the spreading speed of the other also depends on the interspecific nonlinearity. From the viewpoint of population dynamics, our results imply that the predator may play a negative effect on the spreading of the prey while the prey may play a positive role on the spreading of the predator.

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Mathematics Subject Classification: Primary: 35K45, 35K57; Secondary: 92D25.

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