BQL Generalized Inverse Condition for Multiple Transcritical and Pitchfork Bifurcation Theorem

2020 ◽  
pp. 1-8
Author(s):  
Guanqi Liu ◽  
Yuwen Wang
Keyword(s):  
Generalized Inverse ◽  
Pitchfork Bifurcation ◽  
Bifurcation Theorem

Multiple Bifurcations of Synchronized Oscillators With Delays

2005 ◽  
Author(s):  
Yuan Y. Yuan
Keyword(s):  
Local Stability ◽  
Time Delays ◽  
Center Manifold ◽  
Zero Solution ◽  
Pitchfork Bifurcation ◽  
Bifurcation Theorem ◽  
Center Manifold Theorem ◽  
System A ◽  
Normal Form Method ◽  
Theoretical Results

The synchronized oscillator with two discrete time delays is considered. The local stability of the zero solution of this system is investigated by studying the distributions of the eigenvalues of the system. A complete bifurcation analysis is given by employing the center manifold theorem, normal form method and bifurcation theorem. It is shown that the trivial fixed point may lose stability via a transcritical/pitchfork bifurcation, Hopf bifurcation or Bogdanov-Takens bifurcation. Some numerical simulation examples are given for justify the theoretical results.

BIFURCATION ANALYSIS OF DIFFERENTIAL-DIFFERENCE-ALGEBRAIC EQUATIONS

2004 ◽  
Vol 14 (08) ◽  
pp. 2853-2865
Author(s):  
DONGYUN DU ◽  
YUN TANG
Keyword(s):  
Bifurcation Analysis ◽  
Pitchfork Bifurcation ◽  
Algebraic Equations ◽  
Bifurcation Theorem ◽  
Local Bifurcations ◽  
Singularity Induced Bifurcation

The dynamics of differential-difference-algebraic equations is studied. The paper extends the study of the local bifurcations to transcritical and pitchfork bifurcation under certain nondegenerate conditions using Lyapunov–Schmidt reduction. Furthermore, an improved version of singularity induced bifurcation theorem is given in this paper.

Analysis of supercritical pitchfork bifurcation in active magnetic bearing-rotor system with current saturation

2021 ◽  
Vol 104 (1) ◽  
pp. 103-123
Author(s):  
Xiaoshen Zhang ◽  
Zhe Sun ◽  
Lei Zhao ◽  
Xunshi Yan ◽  
Jingjing Zhao ◽  
...  
Keyword(s):  
Pitchfork Bifurcation ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Active Magnetic Bearing ◽  
Current Saturation

Erratum: Generalized Inverse of a Matrix Product

SIAM Review ◽  
1967 ◽  
Vol 9 (2) ◽  
pp. 249-249 ◽  
Author(s):  
T. N. E. Greville
Keyword(s):  
Generalized Inverse ◽  
Matrix Product
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