Non-local stability of a Nash equilibrium seeking scheme with dither re-use

2012 ◽  
Author(s):  
Ronny J. Kutadinata ◽  
William H. Moase ◽  
Chris Manzie
Keyword(s):  
Nash Equilibrium ◽  
Local Stability ◽  
Non Local

scholarly journals Dynamic Cournot Duopoly Game with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. A. Elsadany ◽  
A. E. Matouk
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Local Stability ◽  
Stability Region ◽  
Equilibrium Points ◽  
Cournot Duopoly ◽  
Nash Equilibrium Point ◽  
Dynamical Behaviors ◽  
Delayed System

The delay Cournot duopoly game is studied. Dynamical behaviors of the game are studied. Equilibrium points and their stability are studied. The results show that the delayed system has the same Nash equilibrium point and the delay can increase the local stability region.

scholarly journals Complex Dynamics of a Model with R&D Competition

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2262
Author(s):  
Massimiliano Ferrara ◽  
Tiziana Ciano ◽  
Mariangela Gangemi ◽  
Luca Guerrini
Keyword(s):  
Nash Equilibrium ◽  
Local Stability ◽  
Complex Dynamics ◽  
Two Stage ◽  
Dynamic Behaviors ◽  
Symmetric Structure

The paper analyzes a two-stage oligopoly game of semi-collusion in production described by a system with a symmetric structure. We examine the local stability of a Nash equilibrium and the presence of bifurcations. We discover that the model is capable of exhibiting extremely complicated dynamic behaviors.

scholarly journals On non-local stability properties of extremum seeking control

Automatica ◽  
2006 ◽  
Vol 42 (6) ◽  
pp. 889-903 ◽  
Author(s):  
Ying Tan ◽  
Dragan Nešić ◽  
Iven Mareels
Keyword(s):  
Local Stability ◽  
Extremum Seeking ◽  
Extremum Seeking Control ◽  
Stability Properties ◽  
Non Local

Toward High-Resolution Low-Voltage SEM

1988 ◽  
Vol 46 ◽  
pp. 218-219
Author(s):  
Zhifeng Shao
Keyword(s):  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Limiting Factor ◽  
Operating Voltage ◽  
Probe Radius ◽  
Non Local ◽  
Electron Microscopes ◽  
Image Position ◽  
Scanning Electron Microscopes

Recently, low voltage (≤5kV) scanning electron microscopes have become popular because of their unprecedented advantages, such as minimized charging effects and smaller specimen damage, etc. Perhaps the most important advantage of LVSEM is that they may be able to provide ultrahigh resolution since the interaction volume decreases when electron energy is reduced. It is obvious that no matter how low the operating voltage is, the resolution is always poorer than the probe radius. To achieve 10Å resolution at 5kV (including non-local effects), we would require a probe radius of 5∽6 Å. At low voltages, we can no longer ignore the effects of chromatic aberration because of the increased ratio δV/V. The 3rd order spherical aberration is another major limiting factor. The optimized aperture should be calculated as

Chromatic aberration and low-voltage SEM

1987 ◽  
Vol 45 ◽  
pp. 546-547
Author(s):  
Zhifeng Shao ◽  
A.V. Crewe
Keyword(s):  
Electron Energy ◽  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Primary Electron ◽  
Probe Size ◽  
Non Local ◽  
Optical Treatment ◽  
Electron Microscopes ◽  
Scanning Electron Microscopes

For scanning electron microscopes, it is plausible that by lowering the primary electron energy, one can decrease the volume of interaction and improve resolution. As shown by Crewe /1/, at V0 =5kV a 10Å resolution (including non-local effects) is possible. To achieve this, we would need a probe size about 5Å. However, at low voltages, the chromatic aberration becomes the major concern even for field emission sources. In this case, δV/V = 0.1 V/5kV = 2x10-5. As a rough estimate, it has been shown that /2/ the chromatic aberration δC should be less than ⅓ of δ0 the probe size determined by diffraction and spherical aberration in order to neglect its effect. But this did not take into account the distribution of electron energy. We will show that by using a wave optical treatment, the tolerance on the chromatic aberration is much larger than we expected.

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