Hopf bifurcation analysis for a ratio-dependent predator–prey system with two delays and stage structure for the predator

2014 ◽  
Vol 231 ◽  
pp. 214-230 ◽  
Author(s):  
Lianwang Deng ◽  
Xuedi Wang ◽  
Miao Peng
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Two Delays ◽  
Ratio Dependent

HOPF BIFURCATION ANALYSIS FOR A RATIO-DEPENDENT PREDATOR–PREY SYSTEM INVOLVING TWO DELAYS

2014 ◽  
Vol 55 (3) ◽  
pp. 214-231 ◽  
Author(s):  
E. KARAOGLU ◽  
H. MERDAN
Keyword(s):  
Hopf Bifurcation ◽  
Normal Form Theory ◽  
Predator Prey ◽  
Prey System ◽  
Discrete Delays ◽  
Form Theory ◽  
Two Delays ◽  
Ratio Dependent ◽  
Centre Manifold Theorem ◽  
Analysis Stability

AbstractThe aim of this paper is to give a detailed analysis of Hopf bifurcation of a ratio-dependent predator–prey system involving two discrete delays. A delay parameter is chosen as the bifurcation parameter for the analysis. Stability of the bifurcating periodic solutions is determined by using the centre manifold theorem and the normal form theory introduced by Hassard et al. Some of the bifurcation properties including the direction, stability and period are given. Finally, our theoretical results are supported by some numerical simulations.

Hopf bifurcation analysis of predator–prey model with two delays and disease transmission

2020 ◽  
Vol 13 (07) ◽  
pp. 2050068
Author(s):  
Renxiang Shi
Keyword(s):  
Periodic Solution ◽  
Hopf Bifurcation ◽  
Global Existence ◽  
Bifurcation Analysis ◽  
Disease Transmission ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Two Delays

In this paper, we study the Hopf bifurcation of predator–prey system with two delays and disease transmission. Furthermore, the global existence of bifurcated periodic solution was studied, the influence of disease transmission is given. At last, some simulations are given to support our result.

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.

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