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.

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.

### Robust exponential attractors for singularly perturbed Hodgkin-Huxley equations

#### 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.
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Exponential attractors; Global attractors; Hodgkin-Huxley model; Hyperbolic equations
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: `http://hdl.handle.net/2434/54030`
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