The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms
Applied and Computational Mathematics
Volume 5, Issue 5, October 2016, Pages: 193-201
Received: Oct. 13, 2016; Published: Oct. 13, 2016
Views 2992      Downloads 150
Author
Wang Hailing, Institute of Information Science and Technology, Xiamen University Tan Kah Kee Colledge, Xiamen, China
Article Tools
Follow on us
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.
Keywords
Stage Structure, Reaction-Diffusion Equations, Equilibrium, Stability
To cite this article
Wang Hailing, The Stability Analysis of Two-Species Competition Model with Stage Structure and Diffusion Terms, Applied and Computational Mathematics. Vol. 5, No. 5, 2016, pp. 193-201. doi: 10.11648/j.acm.20160505.12
References
[1]
Chen Lansun, The phase structure of the population dynamics model [J]. Journal of north China university (natural science edition), in June 2000, 1 (3): 185-191.
[2]
Wang Lie, Chen Siyang, Infected with time delay and stage structure vaccination of youth the stability of the single population model [J]. Journal of Shan xi normal university (natural science edition), in January, 2013, 41 (1): 15-19.
[3]
Yan Weilin, Two species competition model with stage structure of the optimal harvesting [J]. Journal of Shanxi university (natural science edition), 2013, 29 (5) in October: 10-12.
[4]
Shi Chunling, Global attractivity in a Lotka-Volterra competition system with feedback controls [J]. Journal of Biomathematics, 2015, 30 (4): 714-720.
[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.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186