Existence and Continuity of Uniform Exponential Attractors of the Singularity Perturbed Hodgkin–Huxley System

In order to show that the standard partially dissipative Hodgkin–Huxley system approximates the hyperbolic Hodgkin–Huxley system for large time, we are interested in establishing the existence of exponential attractors for the hyperbolic system with estimates of the fractal dimension and the rate of attraction of trajectories which are uniform with respect to the perturbation. Furthermore, we obtain the continuity of exponential attractors.