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Volume 10, Number 5, 2020, Pages 2036-2057                                                                DOI:10.11948/20190321
Exponential attractor for Hindmarsh-Rose equations in neurodynamics
Chi Phan,Yuncheng You
Keywords:Diffusive Hindmarsh-Rose equations, exponential attractor, squeezing property, compact absorbing set, finite fractal dimension.
Abstract:
      The existence of exponential attractor for the diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain in the study of neurodynamics is proved through uniform estimates and a new theorem on the squeezing property of the abstract reaction-diffusion equation established in this paper. This result on the exponential attractor infers that the global attractor whose existence has been proved in [22] for the diffusive Hindmarsh-Rose semiflow has a finite fractal dimension.
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