Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions
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Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3
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Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3
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Received:
01 July 2004
Accepted:
29 June 2018
Published:
01 November 2004
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MSC :
92D25, 65M06, 35K57, 41A28.
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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.
Citation: Dong Liang, Jianhong Wu, Fan Zhang. Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions[J]. Mathematical Biosciences and Engineering, 2005, 2(1): 111-132. doi: 10.3934/mbe.2005.2.111
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Abstract
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.
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