A prey-predator model with a free boundary and sign-changing coefficient in time-periodic environment

Meng Zhao; Wan-Tong Li; Jia-Feng Cao

doi:10.3934/dcdsb.2017138

Article Contents

2017, Volume 22, Issue 9: 3295-3316. Doi: 10.3934/dcdsb.2017138

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A prey-predator model with a free boundary and sign-changing coefficient in time-periodic environment

School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China

* Corresponding author
* Corresponding author

Received: September 2016

Revised: December 2016

Published: October 2017

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Abstract

This paper is concerned with a prey-predator model with sign-changing intrinsic growth rate in heterogeneous time-periodic environment, where the prey species lives in the whole space but the predator species lives in a region enclosed by a free boundary. It is shown that the results for the case of the non-periodic environment remain true in time-periodic environment. In fact, we first establish a similar spreading-vanishing dichotomy, which implies that if the predator species could spread successfully, then the two species will coexist, and this is certainly for the situation that the predation is relatively weak. Furthermore, some criteria are also obtained for spreading and vanishing. At last, some rough estimates of the asymptotic spreading speed are given if spreading occurs.

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Mathematics Subject Classification: 35K51, 35R35, 35B40, 92B05.

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