Noise-induced extinction for a ratio-dependent predator–prey model with strong Allee effect in prey

2018 ◽  
Vol 496 ◽  
pp. 40-52 ◽  
Author(s):  
Partha Sarathi Mandal
Keyword(s):  
Allee Effect ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Strong Allee Effect ◽  
Ratio Dependent

Qualitative analysis of a diffusive predator–prey model with Allee and fear effects

2021 ◽  
pp. 2150037
Author(s):  
Jia Liu
Keyword(s):  
Allee Effect ◽  
Sufficient Conditions ◽  
Allee Effects ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Strong Allee Effect ◽  
Spatially Homogeneous ◽  
Fear Effects

In this study, we consider a diffusive predator–prey model with multiple Allee effects induced by fear factors. We investigate the existence, boundedness and permanence of the solution of the system. We also discuss the existence and non-existence of non-constant solutions. We derive sufficient conditions for spatially homogeneous (non-homogenous) Hopf bifurcation and steady state bifurcation. Theoretical and numerical simulations show that strong Allee effect and fear effect have great effect on the dynamics of system.

scholarly journals Stability and Bifurcation in a Predator–Prey Model with the Additive Allee Effect and the Fear Effect

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1280
Author(s):  
Liyun Lai ◽  
Zhenliang Zhu ◽  
Fengde Chen
Keyword(s):  
Allee Effect ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Strong Allee Effect ◽  
Theoretical Results

We proposed and analyzed a predator–prey model with both the additive Allee effect and the fear effect in the prey. Firstly, we studied the existence and local stability of equilibria. Some sufficient conditions on the global stability of the positive equilibrium were established by applying the Dulac theorem. Those results indicate that some bifurcations occur. We then confirmed the occurrence of saddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation. Those theoretical results were demonstrated with numerical simulations. In the bifurcation analysis, we only considered the effect of the strong Allee effect. Finally, we found that the stronger the fear effect, the smaller the density of predator species. However, the fear effect has no influence on the final density of the prey.

Bifurcations and Control in a Discrete Predator–Prey Model with Strong Allee Effect

2018 ◽  
Vol 28 (05) ◽  
pp. 1850062 ◽  
Author(s):  
Limin Zhang ◽  
Lan Zou
Keyword(s):  
Allee Effect ◽  
Hybrid Control ◽  
Approximate Expression ◽  
Point Of View ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Strong Resonance ◽  
Prey Model ◽  
Strong Allee Effect ◽  
The Stability

In this paper, the bifurcations and the control of a discrete predator–prey model with strong Allee effect on the prey are investigated. This shows that the model undergoes a supercritical Neimark–Sacker bifurcation. Meanwhile, the explicit approximate expression of the stable closed invariant curve caused by the Neimark–Sacker bifurcation is given. 1:3 strong resonance is investigated through approximation by a flow, and the bifurcation curves around 1:3 resonance are obtained. Moreover, for the sake of regulating the stability of the biological system, we extend the hybrid control strategy to control the Neimark–Sacker bifurcation and 1:3 strong resonance. The theoretical analyses are validated by numerical simulations and are explained from the biological point of view.

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