American Institute of Mathematical Sciences

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2005, 2(1): 111-132. doi: 10.3934/mbe.2005.2.111

Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions

Dong Liang 1, , Jianhong Wu 2, and  Fan Zhang 2,

1. 

Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada
2. 

Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3, Canada, Canada

Received  July 2004 Revised  September 2004 Published  November 2004

In this paper, we consider the population growth of a single species living in a two-dimensional spatial domain. New reaction-diffusion equation models with delayed nonlocal reaction are developed in two-dimensional bounded domains combining different boundary conditions. The important feature of the models is the reflection of the joint effect of the diffusion dynamics and the nonlocal maturation delayed effect. We consider and analyze numerical solutions of the mature population dynamics with some well-known birth functions. In particular, we observe and study the occurrences of asymptotically stable steady state solutions and periodic waves for the two-dimensional problems with nonlocal delayed reaction. We also investigate numerically the effects of various parameters on the period, the peak and the shape of the periodic wave as well as the shape of the asymptotically stable steady state solution.
Keywords: time delay, numerical analysis., 2-d reaction-diffusion, non-local reac- tion, population growth.
Mathematics Subject Classification: 92D25, 65M06, 35K57, 41A2.
Citation: Dong Liang, Jianhong Wu, Fan Zhang. Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions. Mathematical Biosciences & Engineering, 2005, 2 (1) : 111-132. doi: 10.3934/mbe.2005.2.111
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