Dynamical analysis of a stage structured predator–prey system with impulsive diffusion and generic functional response

The dynamics of a delayed Gompertz model with Holling IV function response and impulsive effects at different moment on the prey

“…Therefore, it is reasonable to introduce the stage structure into the predator-prey models. Many researchers have B Yuanfu Shao shaoyuanfu@163.com 1 incorporated it into biological models, where the stage-structure was modeled by using a time delay [1][2][3][4][5]. These obtained results have shown that stage-structure affects the dynamics and greatly enriches biologic backgrounds.…”

A periodic single species model with intermittent unilateral diffusion in two patches

“…Bifurcations are considered by Peng and Jiang [13]. Stability and permanence were considered by Jiao and Chen [14,15], Shao [16], Liu et al [17], Zhang et al [18], Shao and Li [19], Liu et al [20], Yang and Zhang [21]. In [6], Liu et al proposed the following periodic single-species model with impulsively unilateral diffusion:…”

“…Some of the mathematical models dealt with a single population dispersing among patches (see [1][2][3][4][5][6]). Some of them dealt with competition and predator-prey interactions in patchy environments (see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]). …”

On an Impulsive Food Web System with Mutual Interference and Distributed Time Delay

“…In the past few decades, food web or food chain predatorprey system has been widely studied by many scholars. Many researchers have obtained some classical theoretical knowledge of the predator-prey system and given some practical control strategies, regulation means, and simulation analysis; all these results can be found in these papers [1][2][3][4]. With the evolution and development of the ecological system, the relationships of dynamics between predators and prey will continue to be the significant theme of ecology and mathematics, since its existence and importance.…”