Attractor-preserving control to avoid saddle-node bifurcation

2014 ◽  
Vol 2 ◽  
pp. 150-153
Author(s):  
Daisuke Ito ◽  
Tetsushi Ueta ◽  
Shigeki Tsuji ◽  
Kazuyuki Aihara
Keyword(s):  
Saddle Node Bifurcation ◽  
Saddle Node

BASIN ORGANIZATION PRIOR TO A TANGLED SADDLE-NODE BIFURCATION

1991 ◽  
Vol 01 (01) ◽  
pp. 107-118 ◽  
Author(s):  
MOHAMED S. SOLIMAN ◽  
J. M. T. THOMPSON
Keyword(s):  
Fractal Structure ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Homoclinic Connections

Heteroclinic and homoclinic connections of saddle cycles play an important role in basin organization. In this study, we outline how these events can lead to an indeterminate jump to resonance from a saddle-node bifurcation. Here, due to the fractal structure of the basins in the vicinity of the saddle-node, we cannot predict to which available attractor the system will jump in the presence of even infinitesimal noise.

scholarly journals Global structural stability of a saddle node bifurcation

1978 ◽  
Vol 236 ◽  
pp. 155-155 ◽  
Author(s):  
Clark Robinson
Keyword(s):  
Structural Stability ◽  
Saddle Node Bifurcation ◽  
Saddle Node

Bifurcation analysis of steady natural convection in a tilted cubical cavity with adiabatic sidewalls

2014 ◽  
Vol 756 ◽  
pp. 650-688 ◽  
Author(s):  
J. F. Torres ◽  
D. Henry ◽  
A. Komiya ◽  
S. Maruyama
Keyword(s):  
Natural Convection ◽  
Rotation Axis ◽  
Numerical Technique ◽  
Continuation Method ◽  
Rotation Vector ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Stable Solutions ◽  
The Stability ◽  
Cubical Cavity

AbstractNatural convection in an inclined cubical cavity heated from two opposite walls maintained at different temperatures and with adiabatic sidewalls is investigated numerically. The cavity is inclined by an angle $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\theta $ around a lower horizontal edge and the isothermal wall set at the higher temperature is the lower wall in the horizontal situation ($\theta = 0^\circ $). A continuation method developed from a three-dimensional spectral finite-element code is applied to determine the bifurcation diagrams for steady flow solutions. The numerical technique is used to study the influence of ${\theta }$ on the stability of the flow for moderate Rayleigh numbers in the range $\mathit{Ra} \leq 150\, 000$, focusing on the Prandtl number $\mathit{Pr} = 5.9$. The results show that the inclination breaks the degeneracy of the stable solutions obtained at the first bifurcation point in the horizontal cubic cavity: (i) the transverse stable rolls, whose rotation vector is in the same direction as the inclination vector ${\boldsymbol{\Theta}}$, start from $\mathit{Ra} \to 0$ forming a leading branch and becoming more predominant with increasing $\theta $; (ii) a disconnected branch consisting of transverse rolls, whose rotation vector is opposite to ${\boldsymbol{\Theta}}$, develops from a saddle-node bifurcation, is stabilized at a pitchfork bifurcation, but globally disappears at a critical inclination angle; (iii) the semi-transverse stable rolls, whose rotation axis is perpendicular to ${\boldsymbol{\Theta}}$ at $\theta \to 0^\circ $, develop from another saddle-node bifurcation, but the branch also disappears at a critical angle. We also found the stability thresholds for the stable diagonal-roll and four-roll solutions, which increase with $\theta $ until they disappear at other critical angles. Finally, the families of stable solutions are presented in the $\mathit{Ra}-\theta $ parameter space by determining the locus of the primary, secondary, saddle-node, and Hopf bifurcation points as a function of $\mathit{Ra}$ and $\theta $.

On saddle-node bifurcation and chaos of satellites

1997 ◽  
Vol 30 (8) ◽  
pp. 4881-4886 ◽  
Author(s):  
Peter B. Béda
Keyword(s):  
Bifurcation And Chaos ◽  
Saddle Node Bifurcation ◽  
Saddle Node

scholarly journals Saddle Node Bifurcation Point Analysis of Voltage Stability of IEEE 30-BUS Power System for Removal of Generation through Bacteria Foraging Optimization Algorithm

2018 ◽  
Vol 7 (3.31) ◽  
pp. 36
Author(s):  
Srikanth B. Venkata ◽  
Lakshmi Devi Ai
Keyword(s):  
Power System ◽  
Optimization Algorithm ◽  
Reactive Power ◽  
Reactive Power Compensation ◽  
Bacterial Foraging Optimization ◽  
Saddle Node Bifurcation ◽  
Saddle Node ◽  
Point Analysis ◽  
Bacteria Foraging Optimization Algorithm ◽  
Bacterial Foraging Optimization Algorithm

This paper deals with the identification of instability nodes of IEEE 30 BUS power system to generation removal. Optimal sizing and locations of reactive power compensations are obtained. Firstly one of the generators is assumed to be removed from service and the saddle node bifurcation (SNB) point voltages are evaluated without reactive power compensation. Secondly two generators are assumed to be removed from service and the saddle node point voltage magnitudes are obtained without reactive power compensation. For both cases the study is conducted by placing optimal reactive power compensations at optimal locations using Bacterial Foraging Optimization Algorithm (BFOA).  

Persistence of the saddle-node bifurcation for nonlinear systems with slow unmodeled dynamics

1993 ◽  
Vol 12 (4) ◽  
pp. 533-555 ◽  
Author(s):  
Lazhar Fekih-Ahmed ◽  
Hsiao-Dong Chiang
Keyword(s):  
Nonlinear Systems ◽  
Unmodeled Dynamics ◽  
Saddle Node Bifurcation ◽  
Saddle Node

Coexisting coherent and incoherent domains near saddle-node bifurcation

2015 ◽  
Vol 111 (6) ◽  
pp. 60008 ◽  
Author(s):  
V. K. Chandrasekar ◽  
R. Suresh ◽  
D. V. Senthilkumar ◽  
M. Lakshmanan
Keyword(s):  
Saddle Node Bifurcation ◽  
Saddle Node
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