scholarly journals The impact of state feedback control on a predator-prey model with functional response

2004 ◽  
Vol 4 (3) ◽  
pp. 607-614 ◽  
Author(s):  
Haiying Jing ◽  
◽  
Zhaoyu Yang ◽  
Keyword(s):  
Feedback Control ◽  
Functional Response ◽  
State Feedback ◽  
State Feedback Control ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
The Impact

Role of Fear in a Predator–Prey Model with Beddington–DeAngelis Functional Response

2019 ◽  
Vol 74 (7) ◽  
pp. 581-595 ◽  
Author(s):  
Saheb Pal ◽  
Subrata Majhi ◽  
Sutapa Mandal ◽  
Nikhil Pal
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Functional Response ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Prey Interaction ◽  
Lyapunov Coefficient ◽  
The Stability ◽  
The Impact

AbstractIn the present article, we investigate the impact of fear effect in a predator–prey model, where predator–prey interaction follows Beddington–DeAngelis functional response. We consider that due to fear of predator the birth rate of prey population reduces. Mathematical properties, such as persistence, equilibria analysis, local and global stability analysis, and bifurcation analysis, have been investigated. We observe that an increase in the cost of fear destabilizes the system and produces periodic solutions via supercritical Hopf bifurcation. However, with further increase in the strength of fear, system undergoes another Hopf bifurcation and becomes stable. The stability of the Hopf-bifurcating periodic solutions is obtained by computing the first Lyapunov coefficient. Our results suggest that fear of predation risk can have both stabilizing and destabilizing effects.

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