Four positive periodic solutions to a periodic Lotka–Volterra predatory–prey system with harvesting terms

Periodic Solutions for n-Species Lotka-Volterra Competitive Systems with Pure Delays

“…For example, in [1-3, 12, 14-20], the authors studied existence of positive periodic solutions for population competition systems, in [4,5,8,13,21], the authors studied existence of positive periodic solutions for population cooperative systems, in [9], the authors studied existence of positive periodic solutions for population predator-prey system, and in [6,11], the authors studied existence of positive periodic solutions for single species systems. The continuation theorem is a powerful tool to study the existence of periodic solutions of periodic high-dimensional timedelayed problems.…”

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.…”

Existence of positive periodic solutions for the impulsive Lotka–Volterra cooperative population model with time-delay and harvesting control on time scales

“…The LotkaVolterra ecological population model proposed by Lotka [1] and Volterra [2] is one of the most famous and important population dynamics models described by functional differential equations. Owing to their theoretical and practical significance, Lotka-Volterra systems have been studied extensively [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. To protect the balanced development or sustainable economic benefits of various species in the ecosystem, a number of artificial controls have been applied to the ecosystem.…”