Multiple positive periodic solutions for a non-autonomous stage-structured predatory-prey system with harvesting terms

Existence of four periodic solutions for a generalized delayed ratio-dependent predator–prey system

“…More details of such models, see [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] for details. By using the coincident degree theory developed by Gaines and Mawhin [1], the existence of four periodic solutions for the delayed predator-prey system is established.…”

“…Recently, the powerful and effective method of coincidence degree ( [1]) has been applied to study the existence and multiplicity of periodic solutions in population models (see [2][3][4][5][6][7][8][9][8][9][10][11][12][13][14][15][16][17][18][19][20] for details). However, to the author's knowledge, there is little results considering the existence results of multiple periodic solutions for two-predator (where the two predators are competitive) and one prey biological models.…”

A non-autonomous Leslie–Gower model with Holling type IV functional response and harvesting complexity

“…For the non-autonomous case, Chen [7] proved the existence of two periodic solutions for a model with Holling-IV functional response, and Xia et al [8] obtained some sufficient conditions for the existence of two periodic solutions in a stage-structured predator-prey model. Li et al [9] established the existence of multiple periodic solutions for a stage-structured model with harvesting terms. Wang et al [10] studied the existence of multiple periodic solutions for an impulsive model with a Holling IV type functional response.…”

Dynamical analysis of a ratio-dependent predator–prey model with Holling III type functional response and nonlinear harvesting in a random environment

“…In recent years, the harvesting effects on the dynamics of predator-prey systems have attracted lots of attention and considerable work has been done (see [3][4][5][6][7][8] and the references cited therein). In their papers, an adequate amount of thorough investigation is carried out to study the existence of periodic solutions for biological models with harvesting terms.…”

“…In addition, Gupta et al [9] presented three types of harvesting functions (constant harvesting, proportional harvesting, nonlinear harvesting), and showed that nonlinear harvesting is more realistic than constant harvesting and proportional harvesting. Motivated by [1][2][3][4][5][6][7][8][9][10][11], in this paper, we propose the following ratio-dependent predator-prey system with Holling III type functional response and nonlinear harvesting terms, which therefore is described as: ), (1.1) where x(t) and y(t) represent the population densities at time t, respectively. All parameters involved in the model are positive.…”