Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Asymptotic pattern of a migratory and nonmonotone population model

Pages: 1171 - 1195, Volume 19, Issue 4, June 2014      doi:10.3934/dcdsb.2014.19.1171

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Chufen Wu - Department of Mathematics, Foshan University, Foshan, 528000, China (email)
Dongmei Xiao - Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China (email)
Xiao-Qiang Zhao - Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL A1C 5S7, Canada (email)

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.

Keywords:  Population model, time delay, threshold dynamics, spreading speed, traveling waves.
Mathematics Subject Classification:  Primary: 35K57, 35B40; Secondary: 92B05.

Received: April 2012;      Revised: July 2013;      Available Online: April 2014.