Hopf bifurcation and stability in predator–prey model with a stage-structure for prey

2013 ◽  
Vol 219 (20) ◽  
pp. 10313-10324 ◽  
Author(s):  
Xiao-Ke Sun ◽  
Hai-Feng Huo ◽  
Cao-Chuan Ma
Keyword(s):  
Hopf Bifurcation ◽  
Stage Structure ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Bifurcation And Stability

scholarly journals Hopf bifurcation and stability analysis of the Rosenzweig-MacArthur predator-prey model with stage-structure in prey

2020 ◽  
Vol 17 (4) ◽  
pp. 4080-4097 ◽  
Author(s):  
Lazarus Kalvein Beay ◽  
◽  
Agus Suryanto ◽  
Isnani Darti ◽  
Trisilowati ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Stage Structure ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Bifurcation And Stability

scholarly journals Hopf bifurcation and stability in a Beddington-DeAngelis predator-prey model with stage structure for predator and time delay incorporating prey refuge

2019 ◽  
Vol 17 (1) ◽  
pp. 141-159 ◽  
Author(s):  
Zaowang Xiao ◽  
Zhong Li ◽  
Zhenliang Zhu ◽  
Fengde Chen
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Bifurcation And Stability

Abstract In this paper, we consider a Beddington-DeAngelis predator-prey system with stage structure for predator and time delay incorporating prey refuge. By analyzing the characteristic equations, we study the local stability of the equilibrium of the system. Using the delay as a bifurcation parameter, the model undergoes a Hopf bifurcation at the coexistence equilibrium when the delay crosses some critical values. After that, by constructing a suitable Lyapunov functional, sufficient conditions are derived for the global stability of the system. Finally, the influence of prey refuge on densities of prey species and predator species is discussed.

scholarly journals STABILITY AND HOPF BIFURCATION OF A MODIFIED DELAY PREDATOR-PREY MODEL WITH STAGE STRUCTURE

2018 ◽  
Vol 8 (2) ◽  
pp. 573-597
Author(s):  
Jing Li ◽  
◽  
Shaotao Zhu ◽  
Ruilan Tian ◽  
Wei Zhang ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Stage Structure ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model
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