The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms

Wang Hailing

doi:doi:10.11648/j.acm.20160505.12

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The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms

Wang Hailing

Published in Applied and Computational Mathematics (Volume 5, Issue 5)

Received: 13 October 2016 Published: 13 October 2016

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Abstract

In this paper, the author proposed and considered a reaction-diffusion equation with diffusion terms and stage structure. We discussed the stability of the positive equilibrium. By using the upper-lower solutions and monotone iteration technique, we obtained the zero steady state and the boundary equilibrium were linear unstable and the unique positive steady state was globally asymptotic stability. The traditional results are improved and this result applies to broader frameworks.

Published in	Applied and Computational Mathematics (Volume 5, Issue 5)
DOI	10.11648/j.acm.20160505.12
Page(s)	193-201
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Stage Structure, Reaction-Diffusion Equations, Equilibrium, Stability

References

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[5]	Li Liangchen, Xu Rui, Global stability and bifurcations of a delayed predator-prey model with Holling type II functional response [J]. Journal of natural science of Heilongjiang university, 2016, 33 (3) in June: 328-337.
[6]	Gao Shujing, Global stability of three stage structured single species growth model [J]. Journal of Xinjiang university: Science Edition, 2001, 18 (2): 154-158.
[7]	Liang Zhiqing, Zhaoqiang, The optimal harvesting strategy about a class of single population model with three phase structure [J]. Journal of Yulin normal university (natural science edition), 2005, 26 (3): 1-3.
[8]	Wu Chufen, Global asymptotic stability of a weakly-coupled reaction diffusion system in the three-species model [J]. Journal of South China normal university (natural science edition), 2015, 47 (3): 142-147.
[9]	Mou En, Zhao Chaofeng, Chen Xiaodong, Zhang Qimin, Stability for single population growth model with three-stage structure and time delay [J]. Journal of Chongqing normal university (natural science), 2016, 33 (4): 85-89.
[10]	Gao Shujing, Chen Lansun, Permanence and global stability for single species model with three life stages and time delay [J]. Acta Mathematica Science, 2006, 26A (4): 527-533.
[11]	Li Yuxia, Global asymptotic stability in three-species non-autonomous system with time-delay [J]. Journal of Taiyuan normal university (natural science), 2016, 15 (2): 26-28.
[12]	Song Lingyu, Liu Fumin, Two predator-prey model with stage structure with diffusion is continuous existence of approximate wave-front solutions [J]. Journal of engineering mathematics, 28 October 2011 (5): 671-680.
[13]	Faria T. Stability and bifurcation for a delayed predator-prey model and the effect of diffusion [J]. Journal of Mathematical Analysis and Applications, 2001, 254: 433-463.5.

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APA Style

Wang Hailing. (2016). The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms. Applied and Computational Mathematics, 5(5), 193-201. https://doi.org/10.11648/j.acm.20160505.12

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ACS Style

Wang Hailing. The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms. Appl. Comput. Math. 2016, 5(5), 193-201. doi: 10.11648/j.acm.20160505.12

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AMA Style

Wang Hailing. The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms. Appl Comput Math. 2016;5(5):193-201. doi: 10.11648/j.acm.20160505.12

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@article{10.11648/j.acm.20160505.12,
  author = {Wang Hailing},
  title = {The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {5},
  pages = {193-201},
  doi = {10.11648/j.acm.20160505.12},
  url = {https://doi.org/10.11648/j.acm.20160505.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160505.12},
  abstract = {In this paper, the author proposed and considered a reaction-diffusion equation with diffusion terms and stage structure. We discussed the stability of the positive equilibrium. By using the upper-lower solutions and monotone iteration technique, we obtained the zero steady state and the boundary equilibrium were linear unstable and the unique positive steady state was globally asymptotic stability. The traditional results are improved and this result applies to broader frameworks.},
 year = {2016}
}

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TY  - JOUR
T1  - The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms
AU  - Wang Hailing
Y1  - 2016/10/13
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160505.12
DO  - 10.11648/j.acm.20160505.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 193
EP  - 201
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160505.12
AB  - In this paper, the author proposed and considered a reaction-diffusion equation with diffusion terms and stage structure. We discussed the stability of the positive equilibrium. By using the upper-lower solutions and monotone iteration technique, we obtained the zero steady state and the boundary equilibrium were linear unstable and the unique positive steady state was globally asymptotic stability. The traditional results are improved and this result applies to broader frameworks.
VL  - 5
IS  - 5
ER  -

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Author Information

Wang Hailing

Institute of Information Science and Technology, Xiamen University Tan Kah Kee Colledge, Xiamen, China

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APA Style

Wang Hailing. (2016). The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms. Applied and Computational Mathematics, 5(5), 193-201. https://doi.org/10.11648/j.acm.20160505.12

Copy | Download

ACS Style

Wang Hailing. The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms. Appl. Comput. Math. 2016, 5(5), 193-201. doi: 10.11648/j.acm.20160505.12

Copy | Download

AMA Style

Wang Hailing. The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms. Appl Comput Math. 2016;5(5):193-201. doi: 10.11648/j.acm.20160505.12

Copy | Download

@article{10.11648/j.acm.20160505.12,
  author = {Wang Hailing},
  title = {The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms},
  journal = {Applied and Computational Mathematics},
  volume = {5},
  number = {5},
  pages = {193-201},
  doi = {10.11648/j.acm.20160505.12},
  url = {https://doi.org/10.11648/j.acm.20160505.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20160505.12},
  abstract = {In this paper, the author proposed and considered a reaction-diffusion equation with diffusion terms and stage structure. We discussed the stability of the positive equilibrium. By using the upper-lower solutions and monotone iteration technique, we obtained the zero steady state and the boundary equilibrium were linear unstable and the unique positive steady state was globally asymptotic stability. The traditional results are improved and this result applies to broader frameworks.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms
AU  - Wang Hailing
Y1  - 2016/10/13
PY  - 2016
N1  - https://doi.org/10.11648/j.acm.20160505.12
DO  - 10.11648/j.acm.20160505.12
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 193
EP  - 201
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20160505.12
AB  - In this paper, the author proposed and considered a reaction-diffusion equation with diffusion terms and stage structure. We discussed the stability of the positive equilibrium. By using the upper-lower solutions and monotone iteration technique, we obtained the zero steady state and the boundary equilibrium were linear unstable and the unique positive steady state was globally asymptotic stability. The traditional results are improved and this result applies to broader frameworks.
VL  - 5
IS  - 5
ER  -

Copy | Download