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

DOI10.1142/S0218127407018695zbMath1144.35342OpenAlexW2042862694WikidataQ60143899 ScholiaQ60143899MaRDI QIDQ3511076

Björn Sandstede

Publication date: 4 July 2008

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127407018695

zbMATH Keywords

nonlinear stabilityspectral stability

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Stability in context of PDEs (35B35) Neural networks for/in biological studies, artificial life and related topics (92B20) Nonlinear first-order PDEs (35F20) Perturbations in context of PDEs (35B20) Stability problems for infinite-dimensional dissipative dynamical systems (37L15)

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Cites Work

• Semigroups of linear operators and applications to partial differential equations
• A nonlocal eigenvalue problem for the stability of a traveling wave in a neuronal medium
• Waves, bumps, and patterns in neural field theories
• Traveling waves of a singularly perturbed system of integral-differential equations arising from neuronal networks
• On the Spectrum of C 0 -Semigroups
• Evans Functions for Integral Neural Field Equations with Heaviside Firing Rate Function
• The Evans function for nonlocal equations
• Existence and Stability of Traveling Pulses in a Continuous Neuronal Network

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