Existence and global asymptotic stability of positive almost periodic solutions of a two-species competitive system

Abstract

The asymptotic behavior of an almost periodic competitive system is investigated. By using differential inequality, the module containment theorem and the Lyapunov function, a good understanding of the existence and global asymptotic stability of positive almost periodic solutions is obtained. Finally, an example and numerical simulations are performed for justifying the theoretical results.

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

“…In this paper, we revisit the dynamic behaviors of a two-species competitive system with nonlinear inter-inhibition terms, which was proposed by Wang et al [23]. By using the iterative method, we are able to obtain some more deep results.…”

“…Which means that Theorem C of [23] could not be applied to system (4.1), and one can only obtain the persistent property of system (4.1) from [23]. Obviously, we improve the main results of [23] by deleting unnecessary conditions.…”

“…Recently, Wang et al [23] studied the dynamic behaviors of the following two-species competitive system with nonlinear inter-inhibition terms dy 1 (t) dt = y 1 (t) r 1 (t) − a 1 (t)y 1 − b 1 (t)y 2 1 + y 2 , dy 2 (t) dt = y 2 (t) r 2 (t) − a 2 (t)y 2 − b 2 (t)y 1 1 + y 1 ,…”

“…For more background of system (1.1), we refer the reader to [11,19,[21][22][23]28] and the references cited therein. For an almost periodic function f (t), set …”

“…But for the system itself, this condition may not be necessary. Also, the authors in [23] did not investigated the extinction property of the system (1.2), which is one of the most important topics in the study of population dynamics (see [2-5, 7, 8, 12, 13, 18, 20] and the references therein). Above analysis motivated us to revisit the autonomous case of system(1.2), i.e., system (1.1).…”