scholarly journals Hopf Bifurcation Analysis for a Modified Time-Delay Predator-Prey System with Harvesting

2015 ◽  
Vol 03 (07) ◽  
pp. 771-780
Author(s):  
Yang Ni ◽  
Yan Meng ◽  
Yiming Ding
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Bifurcation Analysis ◽  
Predator Prey ◽  
Prey System

THE EFFECT OF DIFFUSION FOR A PREDATOR–PREY SYSTEM WITH NONMONOTONIC FUNCTIONAL RESPONSE

2004 ◽  
Vol 14 (12) ◽  
pp. 4309-4316 ◽  
Author(s):  
ZHIHUA LIU ◽  
RONG YUAN
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Functional Response ◽  
Bifurcation Analysis ◽  
Predator Prey ◽  
Prey System ◽  
Nonmonotonic Functional Response

We consider the delayed predator–prey system with diffusion. The bifurcation analysis of the model shows that Hopf bifurcation can occur under some conditions and the system has a Bogdanov–Takens singularity for any time delay value.

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 Hopf Bifurcation Analysis of a Predator-Prey Biological Economic System with Nonselective Harvesting

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Biwen Li ◽  
Zhenwei Li ◽  
Boshan Chen ◽  
Gan Wang
Keyword(s):  
Hopf Bifurcation ◽  
Economic System ◽  
Bifurcation Analysis ◽  
Economic Perspective ◽  
Modified Model ◽  
Bifurcation Theorem ◽  
Predator Prey ◽  
Economic Profit ◽  
Prey System ◽  
Nonselective Harvesting

A modified predator-prey biological economic system with nonselective harvesting is investigated. An important mathematical feature of the system is that the economic profit on the predator-prey system is investigated from an economic perspective. By using the local parameterization method and Hopf bifurcation theorem, we analyze the Hopf bifurcation of the proposed system. In addition, the modified model enriches the database for the predator-prey biological economic system. Finally, numerical simulations illustrate the effectiveness of our results.

Hopf Bifurcation Analysis of a Predator Prey System Involving Switching

1996 ◽  
Vol 65 (3) ◽  
pp. 864-867 ◽  
Author(s):  
Q. J. A. Khan ◽  
B. S. Bhatt ◽  
R. P. Jaju
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Predator Prey ◽  
Prey System

Rank One Strange Attractors in Periodically Kicked Predator–Prey System with Time-Delay

2016 ◽  
Vol 26 (07) ◽  
pp. 1640114 ◽  
Author(s):  
Wenjie Yang ◽  
Yiping Lin ◽  
Yunxian Dai ◽  
Huitao Zhao
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Strange Attractors ◽  
Periodic Force ◽  
Delayed Systems ◽  
Predator Prey ◽  
Prey System ◽  
Rank One ◽  
Delayed System ◽  
System With Time Delay

This paper is devoted to the study of the problem of rank one strange attractor in a periodically kicked predator–prey system with time-delay. Our discussion is based on the theory of rank one maps formulated by Wang and Young. Firstly, we develop the rank one chaotic theory to delayed systems. It is shown that strange attractors occur when the delayed system undergoes a Hopf bifurcation and encounters an external periodic force. Then we use the theory to the periodically kicked predator–prey system with delay, deriving the conditions for Hopf bifurcation and rank one chaos along with the results of numerical simulations.

On the Existence of Periodic Solutions of a Three-Patch Diffusion Predator-Prey System

2009 ◽  
Vol 64 (7-8) ◽  
pp. 405-410
Author(s):  
Mohammed Ismail ◽  
Atta A. K. Abu Hany ◽  
Aysha Agha
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Periodic Orbit ◽  
Time Delays ◽  
Positive Equilibrium ◽  
Bifurcation Parameter ◽  
Predator Prey ◽  
Prey System ◽  
Existence Of Periodic Solutions

AbstractWe establish a mathematical model for the three-patch diffusion predator-prey system with time delays. The theory of Hopf bifurcation is implemented, choosing the time delay parameter as a bifurcation parameter. We present the condition for the existence of a periodic orbit of the Hopf-type from the positive equilibrium.

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