Study the Dynamics of Commensalism Interaction with Michaels-Menten Type Prey Harvesting

Abstract

This paper suggests and analyses a model consisting of two commensal populations with Michaelis-Menten type of harvesting for the first population. The first harvested commensal species draws strength from the second hosted species. The overall dynamics are provided to achieve the coexistence, stability and persistence of the equilibrium points for the proposed system. The local bifurcation near the positive equilibrium point is attained. Moreover, numerical simulation using MATLAB is investigated to the impact of the commensalism interaction on the behavior of the planned model. The analysis shows that the role of commensalismpr events the first population from extinction, which could be helpful for the survival of both species.

Dynamic Behaviors of an Obligate Commensal Symbiosis Model with Crowley–Martin Functional Responses

“…During the last decades, many scholars investigated the dynamic behaviors of the commensalism model; see and the references cited therein. Topics such as the stability of the system [1][2][3][4][5][6][7][8][9][10]37], the existence of periodic solution or almost periodic solution [11,15,25,36], the influence of harvesting [1][2][3][12][13][14][26][27][28], the influence of stage structure ( [16]), the influence of Allee effect [9,[17][18][19][20]24,32,33], the bifurcation phenomenon of the system [9,29,32,33], the influence of feedback control [8,23], the persistent property of the system [34,35,37], the influence of commensalism to the ecological network [6,7], and the influence of stochastic disturbance [5] were extensively investigated by many scholars. However, the commensalism model is not well studied in the sense that, to this ...…”

Global Attractivity of Symbiotic Model of Commensalism in Four Populations with Michaelis–Menten Type Harvesting in the First Commensal Populations

“…Some substantial progress has been made in the study of the commensalism system. Topics such as the stability of the system [1][2][3][4][19][20][21]39,40], the persistent and extinction properties of the system [3,19], the existence of a periodic solution or almost periodic solution [6][7][8][9][10]41], the influence of stage structure [10], the influence of Allee effect [11][12][13][14][15][16][17][18][19], the influence of feedback control [19][20][21], the influence of harvesting [5,[27][28][29][30][31][32][33][34][35][36][37][38], the bifurcation phenomenon of the system [4,[18][19][20]26,…”

“…It is well known that the harvesting of species is an effective way for human beings to obtain resources. Already, there are many scholars investigateing the dynamic behaviors of the commensalism model with the influence of linear or nonlinear type harvesting [5,[28][29][30][31][32][33][34][35][36][37][38][39][40]42,45].…”

“…Many scholars [8,27,32,[34][35][36][37][38][39][40][41] argued that the nonlinear harvesting such as Michaelis-Menten type harvesting is more realistic from the biological and economical points of view. Chen [27] proposed and studied the following model for the first time, in which the first species is subject to Michaelis-Menten type harvesting:…”

“…Shireen Jawad [32] proposed the following commensalism model with Michaelis-Menten type harvesting and a Holling II functional response:…”