Dynamic behaviors of two species amensalism model with a cover for the first species


Authors

Xiangdong Xie - Department of Mathematics, Ningde Normal University, Ningde, Fujian, 352300, P. R. China. Fengde Chen - College of Mathematics and Computer Sciences, Fuzhou University, Fuzhou, Fujian, 350116, P. R. China. Mengxin He - College of Mathematics and Computer Sciences, Fuzhou University, Fuzhou, Fujian, 350116, P. R. China.


Abstract

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.


Share and Cite

  • Share on Facebook
  • Share on Twitter
  • Share on LinkedIn
ISRP Style

Xiangdong Xie, Fengde Chen, Mengxin He, Dynamic behaviors of two species amensalism model with a cover for the first species, Journal of Mathematics and Computer Science, 16 (2016), no. 3, 395--401

AMA Style

Xie Xiangdong, Chen Fengde, He Mengxin, Dynamic behaviors of two species amensalism model with a cover for the first species. J Math Comput SCI-JM. (2016); 16(3):395--401

Chicago/Turabian Style

Xie, Xiangdong, Chen, Fengde, He, Mengxin. "Dynamic behaviors of two species amensalism model with a cover for the first species." Journal of Mathematics and Computer Science, 16, no. 3 (2016): 395--401


Keywords


MSC


References