Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances

Abstract

Abstract:A two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]. Numeric simulations are carried out to show the feasibility of our results.

Dynamic Behaviors of a Competitive System with Beddington-DeAngelis Functional Response

“…However, to the best of our knowledge, there are no researches on the dynamic behaviors of continuous analogue of system (7) which is a special case of system (2) under ( ) = 0 and ( ) = 1 ( = 1, 2). Based on the above papers, Chen, Chen and Huang [14] proposed system (2) with the effect of toxic substances and obtained the partial extinction of system. However, authors in [14] did not study some important topics such as permanence, stability, and almost periodic solutions of the system.…”

“…Based on the above papers, Chen, Chen and Huang [14] proposed system (2) with the effect of toxic substances and obtained the partial extinction of system. However, authors in [14] did not study some important topics such as permanence, stability, and almost periodic solutions of the system. Hence, 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).…”

Permanence, partial survival, extinction, and global attractivity of a nonautonomous harvesting Lotka–Volterra commensalism model incorporating partial closure for the populations

“…During the last decades, there are many excellent results on these three topics; see [28][29][30][31][32][33][34][35][36][37] and the references therein. For example, Shi, Li, and Chen [30] studied the extinction property of a competition system with infinite delay and feedback controls; Chen, Xie, and Li [31] investigated the partial extinction of the predator-prey model with stage structure; Chen, Chen, and Huang [32] investigated the extinction property of the nonlinear competition system with Beddington-DeAngelis functional response; Xie, Xue, Wu et al [33] studied the extinction property of a nonlinear toxic substance competition system; Chen, Ma, and Zhang [34] showed that if the refuge is restricted to suitable area, then the Lotka-Volterra predato-prey system can admit a unique positive equilibrium, which is globally attractive. In this paper, we also focus our attention on the persistency, extinction, and stability of system (1.4).…”

Global Attractivity and Extinction of a Discrete Competitive System with Infinite Delays and Single Feedback Control

“…Assume that each species needs some time to mature and the competition occurs after some time lag required for maturity of the species; Gopalsamy [2] discussed the following system with discrete delays: Such systems are not well studied in the sense that most results are continuous time cases related (see [3,4]). As we know, a discrete time system governed by difference equations is more approximate than the continuous ones when the populations have nonoverlapping generations or a short-life expectancy.…”