Robust exponential attractors for singularly perturbed Hodgkin-Huxley equations

DOI10.1016/J.JDE.2008.12.025zbMath1183.35049OpenAlexW2060179428MaRDI QIDQ1022944

Cecilia Cavaterra, Maurizio Grasselli

Publication date: 10 June 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.12.025

zbMATH Keywords

global attractorshyperbolic equationsHodgkin-Huxley modelexponential attractorsneural excitability

Mathematics Subject Classification ID

Attractors (35B41) Singular perturbations in context of PDEs (35B25) Physiology (general) (92C30) Second-order semilinear hyperbolic equations (35L71)

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Cites Work

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• A reaction-diffusion equation with memory
• Singularities and groups in bifurcation theory. Volume I
• On travelling wave solutions of the Hodgkin-Huxley equations
• Existence and continuity of uniform exponential attractors of the singularity perturbed Hodgkin-Huxley system
• Uniform exponential attractors for a singularly perturbed damped wave equation.
• Finite dimensionality and upper semicontinuity of the global attractor of singularly perturbed Hodgkin-Huxley systems
• Numerical studies of the steady-state equations for a Hodgkin-Huxley model
• Double Impulse Solutions in Nerve Axon Equations
• On a model stationary nonlinear wave in an active medium
• An initial-boundary value problem of physiological significance for equations of nerve conduction
• On theory of pulse transmission in a nerve fibre
• Bursting Phenomena in Excitable Membranes
• Convergence of singularly perturbed Hodgkin-Huxley systems
• A construction of a robust family of exponential attractors
• Exponential attractors and finite-dimensional reduction for non-autonomous dynamical systems
• Mathematical Aspects of Hodgkin-Huxley Neural Theory

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