scholarly journals Hopf bifurcation, stability switches and chaos in a prey-predator system with three stage structure and two time delays

2019 ◽  
Vol 16 (6) ◽  
pp. 6934-6961 ◽  
Author(s):  
Shunyi Li ◽  
◽  
Keyword(s):  
Hopf Bifurcation ◽  
Time Delays ◽  
Stage Structure ◽  
Stability Switches ◽  
Bifurcation Stability ◽  
Predator System

Stability and Hopf bifurcation analysis in a prey–predator system with stage-structure for prey and time delay

2008 ◽  
Vol 38 (4) ◽  
pp. 1104-1114 ◽  
Author(s):  
Yuanyuan Chen ◽  
Song Changming
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Bifurcation Analysis ◽  
Stage Structure ◽  
Predator System

scholarly journals Hopf bifurcation analysis in a stage-structure predator–prey model with two time delay

2022 ◽  
Vol 355 ◽  
pp. 03048
Author(s):  
Bochen Han ◽  
Shengming Yang ◽  
Guangping Zeng
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Local Stability ◽  
Time Delays ◽  
Stage Structure ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Predator Model

In this paper, we consider a predator-prey system with two time delays, which describes a prey–predator model with parental care for predators. The local stability of the positive equilibrium is analysed. By choosing the two time delays as the bifurcation parameter, the existence of Hopf bifurcation is studied. Numerical simulations show the positive equilibrium loses its stability via the Hopf bifurcation when the time delay increases beyond a threshold.

Stability and bifurcation analysis for a delayed viral infection model with full logistic proliferation

2020 ◽  
Vol 13 (05) ◽  
pp. 2050033
Author(s):  
Yan Geng ◽  
Jinhu Xu
Keyword(s):  
Hopf Bifurcation ◽  
Viral Infection ◽  
Time Delays ◽  
Infection Model ◽  
Lyapunov Functionals ◽  
Stability Switches ◽  
Two Delays ◽  
Infected Cells ◽  
Bifurcation And Stability ◽  
Viral Infection Model

In this paper, we study a delayed viral infection model with cellular infection and full logistic proliferations for both healthy and infected cells. The global asymptotic stabilities of the equilibria are studied by constructing Lyapunov functionals. Moreover, we investigated the existence of Hopf bifurcation at the infected equilibrium by regarding the possible combination of the two delays as bifurcation parameters. The results show that time delays may destabilize the infected equilibrium and lead to Hopf bifurcation. Finally, numerical simulations are carried out to illustrate the main results and explore the dynamics including Hopf bifurcation and stability switches.

THE ANALYSIS OF HOPF BIFURCATION FOR THE PREY-PREDATOR SYSTEM WITH DIFFUSION AND DELAY

1991 ◽  
Vol 11 (2) ◽  
pp. 142-163 ◽  
Author(s):  
Li Zhou ◽  
Kaitai Song
Keyword(s):  
Hopf Bifurcation ◽  
Predator System

Oscillatory Dynamics of P53 Network With Time Delays

2018 ◽  
Vol 21 (6) ◽  
pp. 411-419 ◽  
Author(s):  
Conghua Wang ◽  
Fang Yan ◽  
Yuan Zhang ◽  
Haihong Liu ◽  
Linghai Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Cell Fate ◽  
Time Delays ◽  
Sustained Oscillation ◽  
Multiple Time ◽  
Cell Fate Decisions ◽  
Oscillatory Dynamics ◽  
Main Components ◽  
Parameter Values ◽  
P53 Network

Aims and Objective: A large number of experimental evidences report that the oscillatory dynamics of p53 would regulate the cell fate decisions. Moreover, multiple time delays are ubiquitous in gene expression which have been demonstrated to lead to important consequences on dynamics of genetic networks. Although delay-driven sustained oscillation in p53-based networks is commonplace, the precise roles of such delays during the processes are not completely known. Method: Herein, an integrated model with five basic components and two time delays for the network is developed. Using such time delays as the bifurcation parameter, the existence of Hopf bifurcation is given by analyzing the relevant characteristic equations. Moreover, the effects of such time delays are studied and the expression levels of the main components of the system are compared when taking different parameters and time delays. Result and Conclusion: The above theoretical results indicated that the transcriptional and translational delays can induce oscillation by undergoing a super-critical Hopf bifurcation. More interestingly, the length of these delays can control the amplitude and period of the oscillation. Furthermore, a certain range of model parameter values is essential for oscillation. Finally, we illustrated the main results in detail through numerical simulations.

scholarly journals A dynamic reaction model of a prey-predator system with stage-structure for predator

2010 ◽  
Vol 4 (5) ◽  
Author(s):  
Tapan Kumar Kar ◽  
Saroj Kumar Chattopadhyay
Keyword(s):  
Stage Structure ◽  
Reaction Model ◽  
Dynamic Reaction ◽  
Predator System

scholarly journals Global Stability and Hopf-bifurcation Analysis of Biological Systems using Delayed Extended Rosenzweig-MacArthur Model

2018 ◽  
Vol 12 (2) ◽  
pp. 171
Author(s):  
Enobong E. Joshua ◽  
Cec Ekemini T. Akpan
Keyword(s):  
Experimental Data ◽  
Population Dynamics ◽  
Hopf Bifurcation ◽  
Asymptotic Stability ◽  
Asymptotically Stable ◽  
Stability Switches ◽  
Large Delay ◽  
Local Hopf Bifurcation ◽  
Delay Margin ◽  
Theoretical Results

This paper investigates the global asymptotic stability of a Delayed Extended Rosenzweig-MacArthur Model via Lyapunov-Krasovskii functionals. Frequency sweeping technique ensures stability switches as the delay parameter increases and passes the critical bifurcating threshold.The model exhibits a local Hopf-bifurcation from asymptotically stable oscillatory behaviors to unstable strange chaotic behaviors dependent of the delay parameter values.Hyper-chaotic fluctuations were observed for large delay values far away from the critical delay margin. Numerical simulations of experimental data obtained via non-dimensionalization have shown the applications of theoretical results in ecological population dynamics.

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