# Exponential Attractor for Hindmarsh-Rose Equations in Neurodynamics

## TL;DR

This paper proves the existence of an exponential attractor for the Hindmarsh-Rose equations, demonstrating finite fractal dimension and advancing understanding of neurodynamic models through new mathematical theorems.

## Contribution

It introduces a new theorem on the squeezing property and establishes the exponential attractor for the Hindmarsh-Rose equations.

## Key findings

- Existence of an exponential attractor proven
- Finite fractal dimension of the global attractor established
- New theorem on reaction-diffusion squeezing property introduced

## Abstract

The existence of an exponential attractor for the diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain originated in the study of neurodynamics is proved through uniform estimates together with a new theorem on the squeezing property of an abstract reaction-diffusion equation also proved in this paper. The results infer that the global attractor whose existence has been established in [23] for the Hindmarsh-Rose semiflow has a finite fractal dimension.