Abstract
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.
Highlights
The predator-prey model is one of the dominant population models, which has been researched extensively to comprehend interactions between various species in a fluctuant natural environment [1] [2] [3] [4] [5]
We have studied the dynamics of a predator-prey model with nonlinear Michaelis-Menten type prey harvesting
Based on relevant mathematical theory, we reveal that nonlinear prey harvesting term plays an important role in influencing the dynamics of model (3)
Summary
The predator-prey model is one of the dominant population models, which has been researched extensively to comprehend interactions between various species in a fluctuant natural environment [1] [2] [3] [4] [5]. [27] systematically studied the dynamics of a Leslie-Gower type predator-prey model with constant-yield predator harvesting They have shown that the model can have various kinds of bifurcations, such as saddle-node bifurcation, Hopf. A ratio-dependent predator-prey model with non-constant predator harvesting rate was analyzed by Lajmiri et al [30] They investigated the stability of equilibria and some bifurcation behaviors. Singh et al [33] proposed a Leslie-Gower predator-prey model with Michaelis-Menten type predator harvesting to explore the stability and bifurcation behaviors. The dynamics of a delayed diffusive predator-prey model with nonlinear predator harvesting has been investigated by Liu and Zhang [36], and they obtained the conditions for Turing and Hopf bifurcation, and found that the delay has remarkable impact on the emergent spatial patterns.
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