Local stability analysis of ratio-dependent predator–prey models with predator harvesting rates

Local stability analysis on Lotka‐Volterra predator‐prey models with prey refuge and harvesting

“…Using suitable transformations to reduce the number of parameters in predator-prey models and susceptible-infective-removed models has been widely used in other works. 4,5,16,19,21,[34][35][36][37] Recall that (x, ) ∈ R 2 is an equilibrium of (4) if it satisfies f (x, y) = 0 and g(x, ) = 0. An equilibrium point (x, y) is said to be positive if x, y ≥ 0 and to be a positive interior equilibrium if x, y > 0.…”

“…One of the classical predator‐prey models is the Lotka‐Volterra predator‐prey model often used to describe the dynamics of biological systems in which two species interact. Since 1925, a variety of predator‐prey models have been proposed by introducing functional responses such as Holling‐Tanner predator responses, Beddington‐DeAngelis functional responses, ratio‐dependent functional responses, and harvesting rates . The dynamical behaviors of these models have been widely investigated and analyzed.…”

“…Since 1925, a variety of predator-prey models have been proposed by introducing functional responses such as Holling-Tanner predator responses, [1][2][3][4][5][6][7][8][9][10][11][12] Beddington-DeAngelis functional responses, [13][14][15][16] ratio-dependent functional responses, [17][18][19][20] and harvesting rates. 5,16,[20][21][22] The dynamical behaviors of these models have been widely investigated and analyzed.…”

“…A variety of constant or nonconstant harvesting rates have been incorporated into predator-prey models, for example, in other works. 5,16,[20][21][22]34 In this paper, we incorporate a constant harvesting rate, denoted by h, into the Lotka-Volterra predator-prey model with prey refuge (1). The proposed model is governed by the following planar system:…”

Qualitative Analysis of a Leslie-Gower Predator-Prey System with Nonlinear Harvesting in Predator

“…Mathematical modeling in harvesting of species was started by Clark [1,2]. There are mainly three types of harvesting according to Gupta et al [3]: (i) ℎ( ) = ℎ, constant rate harvesting (see [4][5][6][7]), (ii) ℎ( ) = , proportionate harvesting (see [8,9]), and (iii) ℎ( ) = /( 1 + 2 ) (Holling type II), nonlinear harvesting (see [10][11][12][13]). Nonlinear harvesting is more realistic and exhibits saturation effects with respect to both the stock abundance and the effort level.…”