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scholarly journals Computing Evans functions numerically via boundary-value problems

2018 ◽  
Vol 367 ◽  
pp. 1-10 ◽  
Author(s):  
Blake Barker ◽  
Rose Nguyen ◽  
Björn Sandstede ◽  
Nathaniel Ventura ◽  
Colin Wahl
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Evans Functions

scholarly journals Evans Functions, Jost Functions, and Fredholm Determinants

2007 ◽  
Vol 186 (3) ◽  
pp. 361-421 ◽  
Author(s):  
Fritz Gesztesy ◽  
Yuri Latushkin ◽  
Konstantin A. Makarov
Keyword(s):  
Fredholm Determinants ◽  
Jost Functions ◽  
Evans Functions

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.

Alternate Evans Functions and Viscous Shock Waves

2001 ◽  
Vol 32 (5) ◽  
pp. 929-962 ◽  
Author(s):  
Sylvie Benzoni-Gavage ◽  
Denis Serre ◽  
Kevin Zumbrun
Keyword(s):  
Shock Waves ◽  
Viscous Shock Waves ◽  
Evans Functions
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