Abstract
This article studies a competitive system with Beddington-DeAngelis functional response and establishes sufficient conditions on permanence, partial extinction, and the existence of a unique almost periodic solution for the system. The results supplement and generalize the main conclusions in recent literature. Numerical simulations have been presented to validate the analytical results.
Highlights
For a continuous bounded function f(t), we define fl = inf f (t), t∈R fu = sup f (t) . (1) t∈RIn the paper, we investigate the dynamic behaviors of the following competitive system: x1̇ (t) = x1 (t) (r1 (t) − a1 (t) x1 (t) − b1 (t) x2 (t)), α1 (t) + β1 (t) x1 (t) + γ1 (t) x2 (t) (2)x2̇ (t) = x2 (t) (r2 (t) − a2 (t) x2 (t) b2 (t) x1 (t) α2 (t) + β2 (t) x1 (t) + γ2 (t) x2 (t) where x1(t) and x2(t) are the biomass of species x1 and x2 at time t, respectively
We investigate the dynamic behaviors of the following competitive system: x1̇ (t) = x1 (t) (r1 (t) − a1 (t) x1 (t) b1 (t) x2 (t)
Discrete Dynamics in Nature and Society and Wang [4] incorporated the impulsive perturbations to the system (4) and investigated the uniqueness of positive almost periodic solutions
Summary
Liu. Discrete Dynamics in Nature and Society and Wang [4] incorporated the impulsive perturbations to the system (4) and investigated the uniqueness of positive almost periodic solutions. Xie et al [6] further considered the partial extinction of system (4) with one toxin producing species. B2 (n) x1 (n) } 1 + x1 (n) and obtained the permanence, stability, and almost periodic solutions of the system. The goal of this paper is to obtain results on permanence, partial extinction, and the existence of a unique almost periodic solution of system (2) and (3). This paper is distributed as follows: Section 2 is devoted to the results on permanence and extinction for system (2).
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