Stability and Bifurcation Analysis of a Predator-Prey Model with Michaelis-Menten Type Prey Harvesting  

作　　者：Wenchang Chen Wenchang Chen(School of Mathematics and Physics, Wenzhou University, Wenzhou, China)

机构地区：[1]School of Mathematics and Physics, Wenzhou University, Wenzhou, China

出　　处：《Journal of Applied Mathematics and Physics》2022年第2期504-526,共23页应用数学与应用物理（英文）

摘　　要：In this paper, we investigated stability and bifurcation behaviors of a predator-prey model with Michaelis-Menten type prey harvesting. Sufficient conditions for local and global asymptotically stability of the interior equilibrium point were established. Some critical threshold conditions for transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation were explored analytically. Furthermore, It should be stressed that the fear factor could not only reduce the predator density, but also affect the prey growth rate. Finally, these theoretical results revealed that nonlinear Michaelis-Menten type prey harvesting has played an important role in the dynamic relationship, which also in turn proved the validity of theoretical derivation.In this paper, we investigated stability and bifurcation behaviors of a predator-prey model with Michaelis-Menten type prey harvesting. Sufficient conditions for local and global asymptotically stability of the interior equilibrium point were established. Some critical threshold conditions for transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation were explored analytically. Furthermore, It should be stressed that the fear factor could not only reduce the predator density, but also affect the prey growth rate. Finally, these theoretical results revealed that nonlinear Michaelis-Menten type prey harvesting has played an important role in the dynamic relationship, which also in turn proved the validity of theoretical derivation.

关 键 词：Michaelis-Menten Type Prey Harvesting Stability Bifurcation Limit Cycle 

分 类 号：O17[理学—数学]