Asymptotic pattern of a migratory and nonmonotone population model

Chufen Wu; Dongmei Xiao; Xiao-Qiang Zhao

doi:10.3934/dcdsb.2014.19.1171

Article Contents

2014, Volume 19, Issue 4: 1171-1195. Doi: 10.3934/dcdsb.2014.19.1171

This issue Previous Article Persistence in some periodic epidemic models with infection age or constant periods of infection Next Article Stochastic averaging principle for dynamical systems with fractional Brownian motion

Asymptotic pattern of a migratory and nonmonotone population model

1.
Department of Mathematics, Foshan University, Foshan, 528000
2.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240
3.
Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7

Received: April 2012

Revised: July 2013

Published: June 2014

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we consider a time-delayed and nonlocal population model with migration and relax the monotone assumption for the birth function. We study the global dynamics of the model system when the spatial domain is bounded. If the spatial domain is unbounded, we investigate the spreading speed $c^*$, the non-existence of traveling wave solutions with speed $c\in(0,c^*)$, the existence of traveling wave solutions with $c\geq c^*$, and the uniqueness of traveling wave solutions with $c>c^*$. It is shown that the spreading speed coincides with the minimal wave speed of traveling waves.

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Mathematics Subject Classification: Primary: 35K57, 35B40; Secondary: 92B05.

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