Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions
In this paper, we consider the population growth of a single speciesliving in a two-dimensional spatial domain. New reaction-diffusionequation models with delayed nonlocal reaction are developed intwo-dimensional bounded domains combining different boundary conditions.The important feature of the mo...
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| Format: | Article |
| Language: | English |
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AIMS Press
2004-10-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.111 |
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| author | Dong Liang Jianhong Wu Fan Zhang |
| author_facet | Dong Liang Jianhong Wu Fan Zhang |
| author_sort | Dong Liang |
| collection | DOAJ |
| description | In this paper, we consider the population growth of a single speciesliving in a two-dimensional spatial domain. New reaction-diffusionequation models with delayed nonlocal reaction are developed intwo-dimensional bounded domains combining different boundary conditions.The important feature of the models is the reflection of the jointeffect of the diffusion dynamics and the nonlocal maturation delayed effect.We consider and analyze numerical solutions of the mature populationdynamics with some well-known birth functions. In particular,we observe and study the occurrences of asymptotically stablesteady state solutionsand periodic waves for the two-dimensional problems withnonlocal delayed reaction. We also investigate numerically theeffects of various parameters on the period, the peak and the shape ofthe periodic wave as well as the shape of the asymptoticallystable steady state solution. |
| format | Article |
| id | doaj-art-c707b90ee8eb481ea256e881818499c6 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2004-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c707b90ee8eb481ea256e881818499c62025-01-24T01:47:55ZengAIMS PressMathematical Biosciences and Engineering1551-00182004-10-012111113210.3934/mbe.2005.2.111Modelling Population Growth with Delayed Nonlocal Reaction in 2-DimensionsDong Liang0Jianhong Wu1Fan Zhang2Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3In this paper, we consider the population growth of a single speciesliving in a two-dimensional spatial domain. New reaction-diffusionequation models with delayed nonlocal reaction are developed intwo-dimensional bounded domains combining different boundary conditions.The important feature of the models is the reflection of the jointeffect of the diffusion dynamics and the nonlocal maturation delayed effect.We consider and analyze numerical solutions of the mature populationdynamics with some well-known birth functions. In particular,we observe and study the occurrences of asymptotically stablesteady state solutionsand periodic waves for the two-dimensional problems withnonlocal delayed reaction. We also investigate numerically theeffects of various parameters on the period, the peak and the shape ofthe periodic wave as well as the shape of the asymptoticallystable steady state solution.https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.111time delaynumerical analysis.2-d reaction-diffusionnon-local reac-tionpopulation growth |
| spellingShingle | Dong Liang Jianhong Wu Fan Zhang Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions Mathematical Biosciences and Engineering time delay numerical analysis. 2-d reaction-diffusion non-local reac-tion population growth |
| title | Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions |
| title_full | Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions |
| title_fullStr | Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions |
| title_full_unstemmed | Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions |
| title_short | Modelling Population Growth with Delayed Nonlocal Reaction in 2-Dimensions |
| title_sort | modelling population growth with delayed nonlocal reaction in 2 dimensions |
| topic | time delay numerical analysis. 2-d reaction-diffusion non-local reac-tion population growth |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.111 |
| work_keys_str_mv | AT dongliang modellingpopulationgrowthwithdelayednonlocalreactionin2dimensions AT jianhongwu modellingpopulationgrowthwithdelayednonlocalreactionin2dimensions AT fanzhang modellingpopulationgrowthwithdelayednonlocalreactionin2dimensions |