Robust exponential attractors for singularly perturbed Hodgkin-Huxley equations |
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Authors: | Cecilia Cavaterra |
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Institution: | a Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via C. Saldini, 50, I-20133 Milano, Italy b Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Via E. Bonardi, 9, I-20133 Milano, Italy |
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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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Keywords: | 35B25 35B41 35L70 92C30 |
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