Dynamic behaviors of a two-species competitive system with nonlinear inter-inhibition terms and infinite delay

Volume 21, Issue 1, pp 45--56 http://dx.doi.org/10.22436/jmcs.021.01.05

Publication Date: March 21, 2020 Submission Date: January 28, 2020 Revision Date: February 12, 2020 Accteptance Date: February 19, 2020

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Authors

Runxin Wu - Mathematics and Physics Institute, Fujian University of Technology, Fuzhou, Fujian, 350014, P. R. China. Zhiqing Gao - College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian, 350116, P. R. China. Fengde Chen - College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian, 350116, 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 \[ \frac{dy_1(t)}{dt} = y_1(t)\Bigg[r_1-a_1y_1-\frac{b_1\int_{-\infty}^{t}K_2(t-s)y_2(s)ds}{1+\int_{-\infty}^{t}K_2(t-s)y_2(s)ds}\Bigg],\ \ \ \frac{dy_2(t)}{dt} = y_2(t)\Bigg[r_2-a_2y_2-\frac{b_2\int_{-\infty}^{t}K_1(t-s)y_1(s)ds}{1+\int_{-\infty}^{t}K_1(t-s)y_1(s)ds}\Bigg], \] where \(r_i, a_i, b_i, i=1,2\) are all positive constants. The results not only improve but also complement the main results of [B. G. Chen, J. Math. Computer Sci., \(\bf 16 \) (2016), 481--494].

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Keywords

• Competition
• nonlinear inter-inhibition terms
• global attractivity
• infinite delay

MSC

•  34C25
•  92D25
•  34D20

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