Dynamic behaviors of a non-selective harvesting Lotka–Volterra amensalism model incorporating partial closure for the populations

Abstract

A non-selective harvesting Lotka-Volterra amensalism model incorporating partial closure for the populations is proposed and studied in this paper. Local and global stability of the boundary and interior equilibria are investigated. By introducing the harvesting, the dynamic behaviors of the system become complicated. Depending on the fraction of the stock available for harvesting, the system maybe extinction, partial survival or two species may coexist in a stable state. Our results supplement and complement the main results of Xiong, Wang, and Zhang (Adv. Appl. Math. 5(2):255-261, 2016).

Allee effect increasing the final density of the species subject to the Allee effect in a Lotka–Volterra commensal symbiosis model

“…During the last decades, many scholars investigated the dynamic behaviors of the mutualism model or commensalism model . Such topics as the stability of the positive equilibrium [1-3, 8-12, 14-17, 19, 20, 24], the persistence of the system [4,6,7,13], the existence of the positive periodic solution [18,21,22,25], the extinction of the species [5,23] etc. have been extensively investigated.…”

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.…”

“…Stimulated by the work [13], Chen [15] proposed the following nonselective harvesting Lotka-Volterra amensalism model incorporating partial closure for the populations:…”

“…Stimulated by the works of Chen [15] and Khajanchi and Banerjee [1], we [36] proposed the following single-species stage structure system incorporating partial closure for the populations and nonselective harvesting:…”

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, many scholars investigated the influence of the harvesting to predator-prey or competition system; see [22][23][24][25][26][27] and the references therein. Chakraborty, Das, and Kar [24] argued that it is necessary to harvest the population but harvesting should be regulated, so that both the ecological sustainability and conservation of the species can be implemented in a long run.…”