On the Analysis of Hopf Bifurcation Associated with a Two-Fold Zero Eigenvalue, Part 2: Nonautonomous System

1999 ◽  
Vol 121 (1) ◽  
pp. 105-109 ◽  
Author(s):  
M. Moh’d ◽  
K. Huseyin
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Autonomous System ◽  
Critical Value ◽  
Harmonic Excitation ◽  
Nonautonomous System ◽  
External Excitation ◽  
Zero Eigenvalue ◽  
Bifurcation And Stability

This paper extends the bifurcation and stability analysis of the autonomous system considered in Part 1 to the case of a corresponding nonautonomous system. The effect of an external harmonic excitation on the Hopf bifurcation is studied via a modified Intrinsic Harmonic Balancing technique. It is observed that a shift in the critical value of the parameter occurs due to the external excitation. The analysis is carried out with the aid of MAPLE which is also instrumental in verifying the consistency of the approximations conveniently.

Hopf Bifurcation and Stability Analysis for a Predator-Prey Model with Delays

2013 ◽  
Vol 850-851 ◽  
pp. 901-904
Author(s):  
Hong Bing Chen ◽  
Li Mei Wang
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Equilibrium Point ◽  
Stable Equilibrium ◽  
Critical Value ◽  
Stable Equilibrium Point ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Necessary And Sufficient ◽  
Bifurcation And Stability

In this paper, a predatorprey model with discrete and distributed delays is investigated. The necessary and sufficient of the stable equilibrium point for this model is studied. Further, analyzed the associated characteristic equation. And, it is found that Hopf bifurcation occurs when τ crosses some critical value. Last, an example showed the feasibility of results.

On the Analysis of Hopf Bifurcation Associated with a Two-Fold Zero Eigenvalue, Part 1: Autonomous System

1999 ◽  
Vol 121 (1) ◽  
pp. 101-104 ◽  
Author(s):  
M. Moh’d ◽  
K. Huseyin
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycles ◽  
Autonomous System ◽  
Periodic Motions ◽  
Zero Eigenvalue ◽  
The Family ◽  
Dynamic Bifurcations ◽  
Formula Type

The static and dynamic bifurcations of an autonomous system associated with a twofold zero eigenvalue (of index one) are studied. Attention is focused on Hopf bifurcation solutions in the neighborhood of such a singularity. The family of limit cycles are analyzed fully by applying the formula type results of the Intrinsic Harmonic Balancing method. Thus, parameter-amplitude and amplitude-frequency relationships as well as an ordered form of approximations for the periodic motions are obtained explicitly. A verification technique, with the aid of MAPLE, is used to show the consistency of ordered approximations.

scholarly journals A nonlinear two-species oscillatory system: bifurcation and stability analysis

2003 ◽  
Vol 2003 (31) ◽  
pp. 1981-1991 ◽  
Author(s):  
Malay Bandyopadhyay ◽  
Rakhi Bhattacharya ◽  
C. G. Chakrabarti
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Wave Train ◽  
Oscillatory System ◽  
Homogeneous System ◽  
Travelling Wave ◽  
Chemical System ◽  
Oscillatory Chemical ◽  
Bifurcation And Stability

The present paper dealing with the nonlinear bifurcation analysis of two-species oscillatory system consists of three parts. The first part deals with Hopf-bifurcation and limit cycle analysis of the homogeneous system. The second consists of travelling wave train solution and its linear stability analysis of the system in presence of diffusion. The last deals with an oscillatory chemical system as an illustrative example.

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
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