Bifurcation and stability analysis of a cross‐diffusion vegetation‐water model with mixed delays

2021 ◽  
Author(s):  
Zixiao Xiong ◽  
Qimin Zhang ◽  
Ting Kang
Keyword(s):  
Stability Analysis ◽  
Water Model ◽  
Mixed Delays ◽  
Cross Diffusion ◽  
Vegetation Water ◽  
Bifurcation And Stability

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.

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.

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