Extinction of a two species competitive system with nonlinear inter-inhibition terms and one toxin producing phytoplankton

Abstract

A two species non-autonomous competitive phytoplankton system with nonlinear inter-inhibition terms and one toxin producing phytoplankton is studied in this paper. Sufficient conditions which guarantee the extinction of a species and the global attractivity of the other one are obtained. Some parallel results corresponding to Yue (Adv. Differ. Equ. 2016Equ. :1, 2016Equ. , doi:10.1007 are established. Numeric simulations are carried out to show the feasibility of our results.

Dynamic Behaviors of a Nonautonomous Impulsive Competitive System with the Effect of Toxic Substance

“…For example, Chen et al [3] and Xie et al [4] considered the global stability of the interior equilibrium point of the competition model of plankton allelopathy. The authors [5][6][7][8][9] discussed the extinction for the competitive model with the effect of toxic substances.…”

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

“…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.…”

“…It is, to the best of the knowledge of the authors, the first time such kind of model proposed. During the last decade, many scholars ( [3][4][5], [8], [11][12][13], [31][32][33][34][35][36][37][38]) investigated the extinction property of the competition system. In this paper, we still focus our attention to the extinction property of the system (1) and (2).…”

Dynamics of a Discrete Allelopathic Phytoplankton Model with Infinite Delays and Feedback Controls

“…As for the almost periodic case, Wang and Liu [2] further investigated the existence, uniqueness, and uniformly asymptotic stability of positive almost periodic solution of system (1). In recent years, many scholars have made great achievements in the competition system with the effect of toxic substance [3,4,[24][25][26]. Yue [3] investigated system (1) with the second species which could be toxic, while the other one is nontoxic.…”