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

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.

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Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations

Biological Cybernetics ◽

10.1007/s004220050031 ◽

1994 ◽

Vol 70 (3) ◽

pp. 267-273

Author(s):

C. Bernard ◽

Y. C. Ge ◽

E. Stockley ◽

J. B. Willis ◽

H. V. Wheal Not Available

Keyword(s):

Differential Equations ◽

Nmda Receptors ◽

Neuronal Network ◽

Network Models ◽

Synaptic Integration

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Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations

Biological Cybernetics ◽

10.1007/bf00197607 ◽

1994 ◽

Vol 70 (3) ◽

pp. 267-273 ◽

Cited By ~ 13

Author(s):

C. Bernard ◽

Y. C. Ge ◽

E. Stockley ◽

J. B. Willis ◽

H. V. Wheal

Keyword(s):

Differential Equations ◽

Nmda Receptors ◽

Neuronal Network ◽

Network Models ◽

Synaptic Integration

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The Barron Space and the Flow-Induced Function Spaces for Neural Network Models

Constructive Approximation ◽

10.1007/s00365-021-09549-y ◽

2021 ◽

Author(s):

Weinan E ◽

Chao Ma ◽

Lei Wu

Keyword(s):

Neural Network ◽

Network Models ◽

Function Spaces ◽

Neural Network Models

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Network Models Made by Dynamic Differential Equations

Procedia Computer Science ◽

10.1016/j.procs.2017.03.091 ◽

2017 ◽

Vol 107 ◽

pp. 466-471 ◽

Cited By ~ 1

Author(s):

Bing Yao ◽

Jing Su ◽

Fei Ma ◽

Xiaomin Wang ◽

Hui Sun ◽

...

Keyword(s):

Differential Equations ◽

Network Models

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Well-posedness of second order degenerate differential equations with infinite delay in Hölder continuous function spaces

Journal of Integral Equations and Applications ◽

10.1216/jie.2021.33.171 ◽

2021 ◽

Vol 33 (2) ◽

Author(s):

Shangquan Bu ◽

Yuchen Zhong

Keyword(s):

Continuous Function ◽

Differential Equations ◽

Infinite Delay ◽

Function Spaces ◽

Second Order ◽

Well Posedness ◽

Hölder Continuous ◽

Order Degenerate ◽

Degenerate Differential Equations

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Solvability of systems of singular partial differential equations in function spaces

Integral Transforms and Special Functions ◽

10.1080/10652460500436627 ◽

2006 ◽

Vol 17 (2-3) ◽

pp. 231-237 ◽

Cited By ~ 3

Author(s):

T. Gramchev ◽

E. Tolis

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Function Spaces ◽

Partial Differential

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Nonlinear Stability of Large Amplitude Traveling Waves to Hyperbolic-parabolic System Modeling Chemotaxis

Series in Contemporary Applied Mathematics - Hyperbolic Problems ◽

10.1142/9789814417099_0052 ◽

2012 ◽

pp. 519-526

Author(s):

Tong Li ◽

Zhi-An Wang

Keyword(s):

Nonlinear Stability ◽

Parabolic System ◽

Traveling Waves ◽

Large Amplitude ◽

System Modeling

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Multi-term fractional integro-differential equations in power growth function spaces

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2021-0032 ◽

2021 ◽

Vol 24 (3) ◽

pp. 739-754

Author(s):

Vu Kim Tuan ◽

Dinh Thanh Duc ◽

Tran Dinh Phung

Keyword(s):

Differential Equations ◽

Laplace Transform ◽

Growth Function ◽

Function Spaces ◽

Power Growth ◽

The Laplace Transform

Abstract In this paper we characterize the Laplace transform of functions with power growth square averages and study several multi-term Caputo and Riemann-Liouville fractional integro-differential equations in this space of functions.

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