scholarly journals An Evans function approach to spectral stability of small-amplitude shock profiles

2004 ◽  
Vol 10 (4) ◽  
pp. 885-924 ◽  
Author(s):  
Ramon Plaza ◽  
◽  
K. Zumbrun ◽  
Keyword(s):  
Small Amplitude ◽  
Spectral Stability ◽  
Evans Function ◽  
Function Approach ◽  
Shock Profiles

EVANS FUNCTIONS AND NONLINEAR STABILITY OF TRAVELING WAVES IN NEURONAL NETWORK MODELS

2007 ◽  
Vol 17 (08) ◽  
pp. 2693-2704 ◽  
Author(s):  
BJÖRN SANDSTEDE
Keyword(s):  
Differential Equations ◽  
Neuronal Network ◽  
Nonlinear Stability ◽  
Traveling Waves ◽  
Network Models ◽  
Function Spaces ◽  
Spectral Stability ◽  
Evans Function ◽  
Evans Functions

Modeling networks of synaptically coupled neurons often leads to systems of integro-differential equations. Particularly interesting solutions in this context are traveling waves. We prove here that spectral stability of traveling waves implies their nonlinear stability in appropriate function spaces, and compare several recent Evans-function constructions that are useful tools when analyzing spectral stability.

scholarly journals Spectral Stability of Weak Relaxation Shock Profiles

2009 ◽  
Vol 34 (2) ◽  
pp. 119-136 ◽  
Author(s):  
Corrado Mascia ◽  
Kevin Zumbrun
Keyword(s):  
Spectral Stability ◽  
Shock Profiles

Stability Analysis in Mean-Field Games via an Evans Function Approach

2018 ◽  
Author(s):  
Piyush Grover
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Mean Field ◽  
Evans Function ◽  
Function Approach ◽  
Mean Field Games ◽  
Mean Field Game ◽  
Large Populations ◽  
Multi Agent ◽  
Hamilton Jacobi Bellman

This work is concerned with stability analysis of stationary and time-varying equilibria in a class of mean-field games that relate to multi-agent control problems of flocking and swarming. The mean-field game framework is a non-cooperative model of distributed optimal control in large populations, and characterizes the optimal control for a representative agent in Nash-equilibrium with the population. A mean-field game model is described by a coupled PDE system of forward-in-time Fokker-Planck (FP) equation for density of agents, and a backward-in-time Hamilton-Jacobi-Bellman (HJB) equation for control. The linear stability analysis of fixed points of these equations typically proceeds via numerical computation of spectrum of the linearized MFG operator. We explore the Evans function approach that provides a geometric alternative to solving the characteristic equation.

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