Robust exponential attractors for singularly perturbed Hodgkin-Huxley equations

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.