Global attractivity of a two-species competitive system with nonlinear inter-inhibition terms


Authors

Baoguo Chen - Research Center for Science Technology and Society, Fuzhou University of International Studies and Trade Fuzhou, Fujian, 350202, P. R. China.


Abstract

Sufficient conditions are obtained for the global attractivity of the positive equilibrium and boundary equilibria of the following two-species competitive system with nonlinear inter-inhibition terms \[\frac{dy_1(t)}{dt}=y_1(t)\left[r_1-a_1y_1-\frac{b_1y_2}{1+y_2}\right],\] \[\frac{dy_2(t)}{dt}=y_2(t)\left[r_2-a_2y_2-\frac{b_2y_1}{1+y_1}\right],\] where \(r_i, a_i, b_i, i = 1, 2\) are all positive constants. Our result shows that conditions which ensure the permanence of the system are almost enough to ensure the global stability of the system. The results not only improve but also complement the main results of Wang et al. [Q. L. Wang, Z. J. Liu, Z. X. Li, R. A. Cheke, Int. J. Biomath., 7 (2014), 18 pages].


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