Comparison and analysis of two forms of harvesting functions in the two-prey and one-predator model

Abstract

A new way to study the harvested predator-prey system is presented by analyzing the dynamics of two-prey and one-predator model, in which two teams of prey are interacting with one team of predators and the harvesting functions for two prey species takes different forms. Firstly, we make a brief analysis of the dynamics of the two subsystems which include one predator and one prey, respectively. The positivity and boundedness of the solutions are verified. The existence and stability of seven equilibrium points of the three-species model are further studied. Specifically, the global stability analysis of the coexistence equilibrium point is investigated. The problem of maximum sustainable yield and dynamic optimal yield in finite time is studied. Numerical simulations are performed using MATLAB from four aspects: the role of the carrying capacity of prey, the simulation about the model equations around three biologically significant steady states, simulation for the yield problem of model system, and the comparison between the two forms of harvesting functions. We obtain that the new form of harvesting function is more realistic than the traditional form in the given model, which may be a better reflection of the role of human-made disturbance in the development of the biological system. MSC: 34D20; 49M30; 92B05

Dynamical behavior of predator–prey model with non-smooth prey harvesting

“…If (x 0 , y 0 ) is in S, then ω(0) µ ζ , and by (7), ω(t) µ ζ for all t 0. Therefore, (x(t), y(t)) ∈ S, ∀t 0.…”

“…Predator-prey systems have long been and will continue to be one of the most important population models that have received extensive attention in both environmental and mathematical ecology [1]. Since the advent of the historic Lotka-Volterra model, this field has attracted many researchers who not only improved their models but also studied and added many more aspects affecting the dynamics of populations [2][3][4][5][6][7][8][9][10][11][12] and wanted to know what models can best represent species interactions.…”

Qualitative Behavior for a Discretized Conformable Fractional-Order Lotka-Volterra Model With Harvesting Effects

“…Moreover, Liu and Huang [5] investigated a harvested predator-prey model using the analysis of two-prey and one-predator system. The occurrence and the attractivity behavior of seven fixed points of these three equations were further presented.…”

Complex Dynamical Analysis of Two Prey−One Predator Model in a Patch Environment Utilizing Spectral Bound

“…Parrish and Saila [16] first proposed a simple mathematical model of the two prey-one predator system which better reflects the diversity of biological systems in nature. Much progress has ever been made in the study of the dynamics of three-dimensional models of two-prey and one-predator [9,14], but the dispersal of species between patches has been not considered in those models. Although dispersal makes the models more complicated, there has been some progress in studying predator-prey models of dispersal in heterogeneous environments.…”