Data di Pubblicazione:
2009
Citazione:
Robust exponential attractors for singularly perturbed Hodgkin-Huxley equations / C. Cavaterra, M. Grasselli. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - 246:12(2009), pp. 4670-4701.
Abstract:
Here we consider a singular perturbation of the Hodgkin–Huxley
system which is derived from the Lieberstein’s model. We study
the associated dynamical system on a suitable bounded phase
space, when the perturbation parameter ε (i.e., the axon specific
inductance) is sufficiently small. We prove the existence of bounded
absorbing sets as well as of smooth attracting sets. We deduce
the existence of a smooth global attractor Aε. Finally we prove
the main result, that is, the existence of a family of exponential
attractors {Eε} which is Hölder continuous with respect to ε.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Exponential attractors; Global attractors; Hodgkin-Huxley model; Hyperbolic equations
Elenco autori:
C. Cavaterra, M. Grasselli
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