Stability and bifurcation analysis in a delay-induced predator-prey model with Michaelis-Menten type predator harvesting

Abstract

The present paper considers a delay-induced predator-prey model with Michaelis-Menten type predator harvesting. The existence of the nontrivial positive equilibria is discussed, and some sufficient conditions for locally asymptotically stability of one of the positive equilibria are developed. Meanwhile, the existence of Hopf bifurcation is discussed by choosing time delays as the bifurcation parameters. Furthermore, the direction of Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations. Finally, some numerical simulations are carried out to support the analytical results.

Bifurcation analysis in a diffusive phytoplankton–zooplankton model with harvesting

“…In several types of harvesting, Michaelis-Menten type harvesting is more realistic from biological and economic points of view [26]. In this paper, we investigate the following model with Michaelis-Menten type prey harvesting:…”

Hopf bifurcation in an age-structured predator–prey system with Beddington–DeAngelis functional response and constant harvesting

“…These results indicate that harvesting on different populations (predators or prey) will induce different nonlinear dynamics and harvesting on predators will result in more complex dynamical behaviors. We refer to Yang and Zhang (2017), Liu et al (2018), Singh and Malik (2021), Yang and Wang (2020a) and Meng and Li (2021) for further studies on delayed predator-prey models with harvesting.…”