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Exponential attractor for Hindmarsh-Rose equations in neurodynamics
Chi Phan,Yuncheng You
Keywords:Hindmarsh-Rose equations, exponential attractor, squeezing property, asymptotic compactness, finite fractal dimension.
Abstract:
      The existence of an exponential attractor for the di usive 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-di usion equation also proved in this paper. The results infer that the global attractor whose existence has been established in [23] for the Hindmarsh-Rose semifow has a finite fractal dimension.