Threshold dynamics of a delayed predator–prey model with impulse via the basic reproduction number

Xiangsen Liu, Binxiang Dai
2018 Advances in Difference Equations  
In this paper, we study a delayed predator-prey model with impulse and, in particular, the existence of the predator-free periodic solution. We employ the approach and techniques coming from epidemiology and calculate the basic reproduction number for the predator. Using the basic reproduction number, we consider the global attraction of the predator-free periodic solution and uniform persistence of the predator. Our results improve the results by Liu (Adv. Differ. Equ. 2016:42, 2016), where
more » ... 42, 2016), where they left the open problem of finding a threshold value that determines the eradication and uniform persistence of the predator. Furthermore, we give some numerical simulations to illustrate our results.
doi:10.1186/s13662-018-1895-1 fatcat:irv3ahhysvenplrx5zbgnkntpm