Note on the stability property of the boundary equilibrium of a May cooperative system with strong and weak cooperative partners
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Authors
Runxin Wu
- School of Mathematics and Physics, Fujian University of Technology, Fuzhou, Fujian 350014, China.
Lin Li
- School of Mathematics and Physics, Fujian University of Technology, Fuzhou, Fujian 350014, China.
Abstract
In this paper, we revisit the stability property of the boundary equilibrium of a May cooperative system with strong and weak cooperative partners.
Our result essentially improves the corresponding result of Zhao et al. [L. Zhao, B. Qin, F. D. Chen, Adv. Difference Equ., \(\textbf{2018}\) (2018), 13 pages].
Share and Cite
ISRP Style
Runxin Wu, Lin Li, Note on the stability property of the boundary equilibrium of a May cooperative system with strong and weak cooperative partners, Journal of Mathematics and Computer Science, 20 (2020), no. 1, 58--63
AMA Style
Wu Runxin, Li Lin, Note on the stability property of the boundary equilibrium of a May cooperative system with strong and weak cooperative partners. J Math Comput SCI-JM. (2020); 20(1):58--63
Chicago/Turabian Style
Wu, Runxin, Li, Lin. "Note on the stability property of the boundary equilibrium of a May cooperative system with strong and weak cooperative partners." Journal of Mathematics and Computer Science, 20, no. 1 (2020): 58--63
Keywords
- Cooperative system
- boundary equilibrium
- global stability
MSC
References
-
[1]
F. D. Chen, On a nonlinear nonautonomous predator-prey model with diffusion and distributed delay, J. Comput. Appl. Math., 180 (2005), 33--49
-
[2]
B. G. Chen, Dynamic behaviors of a commensal symbiosis model involving Allee effect and one party can not survive independently, Adv. Difference Equ., 2018 (2018), 12 pages
-
[3]
B. G. Chen, The influence of commensalism on a Lotka-Volterra commensal symbiosis model with Michaelis-Menten type harvesting, Adv. Difference Equ., 2019 (2019), 14 pages
-
[4]
F. D. Chen, H. L. Wu, X. D. Xie, Global attractivity of a discrete cooperative system incorporating harvesting, Adv. Difference Equ., 2016 (2016), 12 pages
-
[5]
L. J. Chen, X. D. Xie, Permanence of an $N$-species cooperation system with continuous time delays and feedback controls, Nonlinear Anal. Real World Appl., 12 (2001), 34--38
-
[6]
F. D. Chen, X. D. Xie, X. F. Chen, Dynamic behaviors of a stage structured cooperation model, Commun. Math. Biol. Neurosci., 2015 (2015), 19 pages
-
[7]
F. D. Chen, Y. L. Xue, Q. F. Lin, X. D. Xie, Dynamic behaviors of a Lotka Volterra commensal symbiosis model with density dependent birth rate, Adv. Difference Equ., 2018 (2018), 14 pages
-
[8]
R. Y. Han, X. D. Xie, F. D. Chen, Permanence and global attractivity of a discrete pollination mutualism in plant pollinator system with feedback controls, Adv. Difference Equ., 2016 (2016), 17 pages
-
[9]
C. Q. Lei, Dynamic behaviors of a stage structured commensalism system, Adv. Difference Equ., 2018 (2018), 20 pages
-
[10]
X. P. Li, W. S. Yang, Permanence of a discrete model of mutualism with infinite deviating arguments, Discrete Dyn. Nat. Soc., 2010 (2010), 7 pages
-
[11]
Y. K. Li, T. W. Zhang, Permanence of a discrete $n$-species cooperation system with time-varying delays and feedback controls, Math. Comput. Modelling, 53 (2011), 1320--1330
-
[12]
Q. F. Lin, Allee effect increasing the final density of the species subject to the Allee effect in a Lotka Volterra commensal symbiosis model, Adv. Difference Equ., 2018 (2018), 9 pages
-
[13]
Z. J. Liu, J. H. Wu, R. H. Tan, Y. P. Chen, Modeling and analysis of a periodic delayed two species model of facultative mutualism, Appl. Math. Comput., 217 (2010), 893--903
-
[14]
Y. Liu, X. D. Xie, Q. F. Lin, Permanence, partial survival, extinction, and global attractivity of a nonautonomous harvesting Lotka Volterra commensalism model incorporating partial closure for the populations, Adv. Difference Equ., 2018 (2018), 16 pages
-
[15]
H. Mohammadi, M. Mahzoon, Effect of weak prey in Lesile-Gower predator-prey model, Appl. Math. Comput., 224 (2013), 196--204
-
[16]
X. D. Xie, F. D. Chen, Y. L. Xue, Note on the stability property of a cooperative system incorporating harvesting, Discrete Dyn. Nat. Soc., 2014 (2014), 5 pages
-
[17]
X. D. Xie, F. D. Chen, K. Yang, Y. L. Xue, Global attractivity of an integrodifferential model of mutualism, Abstr. Appl. Anal., 2014 (2014), 6 pages
-
[18]
X. D. Xie, Y. L. Xue, R. X. Wu, Global attractivity in a discrete mutualism model with infinite deviating arguments, Discrete Dyn. Nat. Soc., 2017 (2017), 8 pages
-
[19]
Y. L. Xue, X. D. Xie, F. D. Chen, R. Y. Han, Almost periodic solution of a discrete commensalism system, Discrete Dyn. Nat. Soc., 2015 (2015), 11 pages
-
[20]
W. S. Yang, X. P. Li, Permanence of a discrete nonlinear N-species cooperation system with time delays and feedback controls, Appl. Math. Comput., 218 (2011), 3581--3586
-
[21]
K. Yang, Z. S. Miao, F. D. Chen, X. D. Xie, Influence of single feedback control variable on an autonomous Holling II type cooperative system, J. Math. Anal. Appl., 435 (2016), 874--888
-
[22]
K. Yang, X. D. Xie, F. D. Chen, Global stability of a discrete mutualism model, Abstr. Appl. Anal., 2014 (2014), 7 pages
-
[23]
L. Y. Yang, X. D. Xie, F. D. Chen, Dynamic behaviors of a discrete periodic predator prey mutualist system, Discrete Dyn. Nat. Soc., 2015 (2015), 11 pages
-
[24]
L. Y. Yang, X. D. Xie, F. D. Chen, Y. L. Xue, Permanence of the periodic predator prey mutualist system, Adv. Difference Equ., 2015 (2015), 15 pages
-
[25]
L. Zhao, B. Qin, F. D. Chen, Permanence and global stability of a May cooperative system with strong and weak cooperative partners, Adv. Difference Equ., 2018 (2018), 13 pages