Extinction in two species nonautonomous nonlinear competitive system

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

“…During the last decade, many scholars paid attention to the extinction property of the competition system, in their series work, Li and Chen [3][4][5][6][7], Chen et al [8,9] studied the extinction property of the competition system with toxic substance. He et al [31], Chen et al [34,35] studied the extinction property of the Gilpin-Ayala competition model.…”

“…The aim of this paper is, by developing the analysis technique of [1,8,9], to investigate the extinction property of the system (1) and (2). The remaining part of this paper is organized as follows.…”

“…For more work on competitive system with toxic substance, one could refer to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][35][36][37][38] and the references cited therein. On the other hand, based on the traditional Lotka-Volterra competition model, some scholars argued that the more appropriate competition model should with nonlinear inter-inhibition terms.…”

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.…”

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.…”