Multiple spatial coherence resonance induced by the stochastic signal in neuronal networks near a saddle-node bifurcation

2010 ◽  
Vol 389 (13) ◽  
pp. 2642-2653 ◽  
Author(s):  
Zhi-Qiang Liu ◽  
Hui-Min Zhang ◽  
Yu-Ye Li ◽  
Cun-Cai Hua ◽  
Hua-Guang Gu ◽  
...  
Keyword(s):  
Neuronal Networks ◽  
Spatial Coherence ◽  
Coherence Resonance ◽  
Saddle Node Bifurcation ◽  
Stochastic Signal ◽  
Saddle Node

COHERENCE RESONANCE–INDUCED STOCHASTIC NEURAL FIRING AT A SADDLE-NODE BIFURCATION

2011 ◽  
Vol 25 (29) ◽  
pp. 3977-3986 ◽  
Author(s):  
HUAGUANG GU ◽  
HUIMIN ZHANG ◽  
CHUNLING WEI ◽  
MINGHAO YANG ◽  
ZHIQIANG LIU ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Point ◽  
Firing Pattern ◽  
Neuronal System ◽  
Neural Firing ◽  
Coherence Resonance ◽  
Saddle Node Bifurcation ◽  
Hopf Bifurcation Point ◽  
Firing Patterns ◽  
Saddle Node

Coherence resonance at a saddle-node bifurcation point and the corresponding stochastic firing patterns are simulated in a theoretical neuronal model. The characteristics of noise-induced neural firing pattern, such as exponential decay in histogram of interspike interval (ISI) series, independence and stochasticity within ISI series are identified. Firing pattern similar to the simulated results was discovered in biological experiment on a neural pacemaker. The difference between this firing and integer multiple firing generated at a Hopf bifurcation point is also given. The results not only revealed the stochastic dynamics near a saddle-node bifurcation, but also gave practical approaches to identify the saddle-node bifurcation and to distinguish it from the Hopf bifurcation in neuronal system. In addition, many previously observed firing patterns can be attribute to stochastic firing pattern near such a saddle-node bifurcation.

SPATIAL COHERENCE RESONANCE IN DELAYED HODGKIN–HUXLEY NEURONAL NETWORKS

2010 ◽  
Vol 24 (09) ◽  
pp. 1201-1213 ◽  
Author(s):  
QING YUN WANG ◽  
MATJAŽ PERC ◽  
ZHI SHENG DUAN ◽  
GUAN RONG CHEN
Keyword(s):  
Information Transmission ◽  
Noise Level ◽  
Neuronal Networks ◽  
Spatial Coherence ◽  
Spatial Dynamics ◽  
Small World ◽  
Transmission Delay ◽  
Small World Networks ◽  
Coherence Resonance ◽  
Short Delay

We study the phenomenon of spatial coherence resonance (SCR) on Hodgkin–Huxley (HH) neuronal networks that are characterized with information transmission delay. In particular, we examine the ability of additive Gaussian noise to optimally extract a particular spatial frequency of excitatory waves in diffusive and small-world networks on which information transmission amongst directly connected neurons is not instantaneous. On diffusively coupled HH networks, we find that for short delay lengths, there always exists an intermediate noise level by which the noise-induced spatial dynamics is maximally ordered, hence implying the possibility of SCR in the system. Importantly thereby, the noise level warranting optimally ordered excitatory waves increases linearly with the increasing delay time, suggesting that extremely long delays might nevertheless preclude the observation of SCR on diffusive networks. Moreover, we find that the small-world topology introduces another obstacle for the emergence of ordered spatial dynamics out of noise because the magnitude of SCR fades progressively as the fraction of rewired links increases, hence evidencing decoherence of noise-induced spatial dynamics on delayed small-world HH networks. Presented results thus provide insights that could facilitate the understanding of the joint impact of noise and information transmission delay on realistic neuronal networks.

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.

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 $.

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).  

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