Dynamic behaviors of a commensal symbiosis model with ratio-dependent functional response and one party can not survive independently
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Authors
Runxin Wu
- College of Mathematics and Physics, Fujian University of Technology, Fuzhou, Fujian, 350014, P. R. China.
Lin Li
- College of Mathematics and Physics, Fujian University of Technology, Fuzhou, Fujian, 350014, P. R. China.
Abstract
We propose a two-species commensal symbiosis model with ratio-dependent functional response
\[\frac{dx}{dt}=x\left(-a_1-b_1x+\frac{c_1y}{x+y}\right),\]
\[\frac{dy}{dt}=y\left(a_2-b_2y\right),\]
For autonomous case, we show that the unique positive equilibrium is globally stable if \(a_1 < c_1\) holds,
and the boundary equilibrium \((0, \frac{a_2}{b_2})\) is globally stable if \(a_1 > c_1\) holds. For nonautonomous case,
some sufficient conditions which ensure the permanence and global attractivity of the system are
obtained. Numeric simulations are carried out to show the feasibility of the main results.
Share and Cite
ISRP Style
Runxin Wu, Lin Li, Dynamic behaviors of a commensal symbiosis model with ratio-dependent functional response and one party can not survive independently, Journal of Mathematics and Computer Science, 16 (2016), no. 4, 495-506
AMA Style
Wu Runxin, Li Lin, Dynamic behaviors of a commensal symbiosis model with ratio-dependent functional response and one party can not survive independently. J Math Comput SCI-JM. (2016); 16(4):495-506
Chicago/Turabian Style
Wu, Runxin, Li, Lin. "Dynamic behaviors of a commensal symbiosis model with ratio-dependent functional response and one party can not survive independently." Journal of Mathematics and Computer Science, 16, no. 4 (2016): 495-506
Keywords
- Commensal symbiosis model
- stability.
MSC
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