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Spatial dynamics of a lattice population model with two age classes and maturation delay

Published online by Cambridge University Press:  06 November 2014

SHI-LIANG WU ,
PEIXUAN WENG  and
SHIGUI RUAN
SHI-LIANG WU
Affiliation:
School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi 710071, People's Republic of China email: slwu@xidian.edu.cn
PEIXUAN WENG
Affiliation:
School of Mathematics, South China Normal University Guangzhou, Guangdong 510631, People's Republic of China email: wengpx@scnu.edu.cn
SHIGUI RUAN
Affiliation:
Department of Mathematics, University of Miami, P.O. Box 249085, Coral Gables, FL 33124–4250, USA email: ruan@math.miami.edu
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Abstract

This paper is concerned with the spatial dynamics of a monostable delayed age-structured population model in a 2D lattice strip. When there exists no positive equilibrium, we prove the global attractivity of the zero equilibrium. Otherwise, we give some sufficient conditions to guarantee the global attractivity of the unique positive equilibrium by establishing a series of comparison arguments. Furthermore, when those conditions do not hold, we show that the system is uniformly persistent. Finally, the spreading speed, including the upward convergence, is established for the model without the monotonicity of the growth function. The linear determinacy of the spreading speed and its coincidence with the minimal wave speed are also proved.

Keywords

population model in 2D lattice stripglobal attractivityspreading speedtravelling waveslinear determinacy

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 26 , Issue 1 , February 2015 , pp. 61 - 91
Copyright
Copyright © Cambridge University Press 2014 

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