A commensal symbiosis model with Holling type functional response

Abstract

A two species commensal symbiosis model with Holling type functional response takes the formis investigated, where a i , b i , i = 1, 2, p and c 1 are all positive constants, p ≥ 1. Local and global stability property of the equilibria is investigated. We also show that depending on the ratio of a 2 b 2 , the first component of the positive equilibrium x

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

“…Recently, many scholars [12][13][14][15][16][17][18][19][20][21] studied the dynamic behavior of the commensalism model; however, none of them consider the influence of harvesting. Stimulated by the recent works of Chakraborty, Das, and Kar [24], we propose a nonautonomous nonselective commensalism model incorporating partial closure to the population.…”

“…Only recently scholars paid attention to such a kind of relationship; see [12][13][14][15][16][17][18][19][20] and the references therein. Topics such as the existence of the positive periodic solution [17], the existence of a positive almost periodic solution [14], the existence and stability of the positive equilibrium [16], the influence of the impulsive [15] were investigated, and many excellent results were obtained. However, as was pointed out by Georgescu and Maxin [20], "One would think that the stability of the coexisting equilibria for two-species models of commensalism would follow immediately from the corresponding results for models of mutualism, when these results are available, .…”

Dynamic behaviors of a stage-structured commensalism system

“…Li et al [21] studied the positive periodic solution of a discrete commensalism model with Holling II functional response. Wu [13] argued that it may be more suitable to assume that the relationship between two species is of nonlinear type instead of linear one, and she established the following two species commensal symbiosis model:…”

“…where a i , b i , i = 1, 2, p and c 1 are all positive constants, p ≥ 1. The results of [13] were then generalized by Wu et al [12] to the following commensalism model with Allee effect:…”

Dynamic behaviors of a stage structure amensalism system with a cover for the first species

“…The second species satisfies the logistic model. During the last decades, many scholars investigated the dynamic behavior of the commensalism or amensalism model [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Such topics as the local stability of the equilibrium [2-4, 7, 8, 10-16, 18, 19], the existence of the positive periodic solution [5,17] the existence and stability of the almost periodic solution [6], extinction of the species [8,11,14], and the influence of the cover [14,16,18] have been studied, and many excellent results are obtained.…”