Exponential stability of traveling pulse solutions of a singularly perturbed system of integral differential equations arising from excitatory neuronal networks

DOI10.1007/s10255-004-0168-9zbMath1072.35022OpenAlexW1970935226MaRDI QIDQ705082

Linghai Zhang

Publication date: 25 January 2005

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-004-0168-9

zbMATH Keywords

eigenvalue problemseigenvalue functionsintegral differential equations

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Neural biology (92C20)

Related Items (2)

Existence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks. ⋮ Recent progress in study of singular perturbation problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the stability of waves of nonlinear parabolic systems
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Dynamics of pattern formation in lateral-inhibition type neural fields
• Multidimensional nonlinear diffusion arising in population genetics
• Mathematical physiology
• Traveling waves in a convolution model for phase transitions
• Tango waves in a bidomain model of fertilization calcium waves
• Stability of front solutions in inhomogeneous media
• On stability of traveling wave solutions in synaptically coupled neuronal networks.
• Existence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks.
• Stability of solutions of nonlinear equations
• Propagating Activity Patterns in Thalamic Neuronal Networks
• Spatially Structured Activity in Synaptically Coupled Neuronal Networks: I. Traveling Fronts and Pulses
• Stability of Planar Wave Solutions to a Combustion Model
• Propagation Phenomena in a Bistable Reaction-Diffusion System
• On the stability theory of solitary waves
• Existence and uniqueness of travelling waves for a neural network
• Wave propagation under curvature effects in a heterogeneous medium
• Stability of multiple-pulse solutions
• Travelling waves for a nonlocal double-obstacle problem

This page was built for publication: Exponential stability of traveling pulse solutions of a singularly perturbed system of integral differential equations arising from excitatory neuronal networks