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Global dynamics of the diffusive and partly diffusive Hindmarsh-Roseequations on a three-dimensional bounded domain originated in neurodynamics areinvestigated in this paper. The existence of global attractors as well as theregularity are proved through various uniform estimates showing the dissipativeproperties and the asymptotically compact characteristics, especially for thepartly diffusive Hindmarsh-Rose equations by means of the Kolmogorov-Riesztheorem.

Global Attractors for Hindmarsh-Rose Equations in Neurodynamics