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Exponential attractor for Hindmarsh-Rose equations in neurodynamics. (English) Zbl 1460.35049

Summary: 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 [the authors and J. Su,“Global attractors for Hindmarsh-Rose equationsin neurodynamics”, Preprint, arXiv:1907.13225] for the diffusive Hindmarsh-Rose semiflow has a finite fractal dimension.

MSC:

35B41 Attractors
35K51 Initial-boundary value problems for second-order parabolic systems
35K57 Reaction-diffusion equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
37N25 Dynamical systems in biology
92C20 Neural biology
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References:

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