Analysis of a delayed predator–prey system with impulsive diffusion between two patches

Coexistence for an Almost Periodic Predator-Prey Model with Intermittent Predation Driven by Discontinuous Prey Dispersal

“…Currently, theories of impulsive differential equations [16] have been introduced into population dynamics. A large number of models have been described by impulsive diffusion (see [14,[17][18][19][20][21][22][23][24]) during the past couple of decades.…”

“…Shao [23] considered the following predator-prey models with impulsive prey diffusion between two patches: …”

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

“…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]). …”

“…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:…”

Mathematical analysis of a delayed stage-structured predator–prey model with impulsive diffusion between two predators territories

“…Recently, increased attention has been given to the dynamics of a large number of mathematical models with impulsive diffusion between two patches (Jiao, 2010a,b;Jiao et al, 2010Jiao et al, , 2009Wang and Chen, 1997;Shao, 2010;Liu et al, 2010;Wang et al, 2007). The most significant topics in the study of population diffusion models are the coexistence of populations, the local and global stability of all possible equilibria and the existence of periodic solutions.…”