Spatial dynamics of a diffusive predator-prey model with stage structure

Liang  Zhang; Zhi-Cheng Wang

doi:10.3934/dcdsb.2015.20.1831

Article Contents

2015, Volume 20, Issue 6: 1831-1853. Doi: 10.3934/dcdsb.2015.20.1831

This issue Previous Article Transversality for time-periodic competitive-cooperative tridiagonal systems Next Article

Spatial dynamics of a diffusive predator-prey model with stage structure

Liang Zhang^1, and
Zhi-Cheng Wang^2,

1.
School of Mathematics and Statistics, Lanzhou University , and Key Laboratory of Applied Mathematics and Complex Systems of Gansu province, Lanzhou, Gansu 730000
2.
School of Mathematics and Statistics, Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou, Gansu 730000

Received: September 30, 2013

Revised: March 31, 2014

Published: July 2015

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Abstract

In this paper, we propose a nonlocal and time-delayed reaction-diffusion predator-prey model with stage structure. It is assumed that prey individuals undergo two stages, immature and mature, and the conversion of consumed prey biomass into predator biomass has a retardation. In terms of the principal eigenvalue of nonlocal elliptic eigenvalue problems, we establish the uniform persistence and global extinction for the model. In particular, the uniform persistence implies the existence of positive steady states. Finally, we investigate a specially spatially homogeneous predator-prey system and show the complicated dynamics of the system due to the non-local delay in the prey equation.

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Mathematics Subject Classification: 35K57, 35B35, 35B40, 92D25, 93B60.

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