TY - JOUR
AU - Xie, Xiangdong
AU - Chen, Fengde
AU - He, Mengxin
PY - 2016
TI - Dynamic behaviors of two species amensalism model with a cover for the first species
JO - Journal of Mathematics and Computer Science
SP - 395--401
VL - 16
IS - 3
AB - In this paper, a two species amensalism model with a cover for the first species takes the form
\[\frac{dx}{dt}=a_1x(t)-b_1x^2(t)-c_1(1-k)x(t)y(t),\]
\[\frac{dy}{dt}=a_2y(t)-b_2y^2(t),\]
is investigated, where \(a_i, b_i, i = 1, 2\) and \(c_1\) are all positive constants, \(k\) is a cover provided for the
species \(x\), and \(0 < k < 1\). Our study shows that if \(0 \leq k < 1-\frac{a_1b_2}{a_2c_1}\),
then \(E_2(0, \frac{a_2}{b_2})\) is globally stable,
and if \(1>k>1-\frac{a_1b_2}{a_2c_1}\), then \(E_3(x^*, y^*)\) is the unique globally stable positive equilibrium. More
precisely, the conditions which ensure the local stability of \(E_2(0, \frac{a_2}{b_2})\)
is enough to ensure its global
stability, and once the positive equilibrium exists, it is globally stable. Some numerical simulations
are carried out to illustrate the feasibility of our findings.
SN - ISSN 2008-949X
UR - http://dx.doi.org/10.22436/jmcs.016.03.09
DO - 10.22436/jmcs.016.03.09
ID - Xie2016
ER -