  Global dynamics of the diffusive and partly diffusive Hindmarsh-Rose
equations on a three-dimensional bounded domain originated in neurodynamics are
investigated in this paper. The existence of global attractors as well as the
regularity are proved through various uniform estimates showing the dissipative
properties and the asymptotically compact characteristics, especially for the
partly diffusive Hindmarsh-Rose equations by means of the Kolmogorov-Riesz
theorem.
