EXPONENTIAL ATTRACTOR FOR HINDMARSH-ROSE EQUATIONS IN NEURODYNAMICS

Chi Phan; Yuncheng You

doi:10.11948/20190321

2020 Volume 10 Issue 5

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Chi Phan, Yuncheng You. EXPONENTIAL ATTRACTOR FOR HINDMARSH-ROSE EQUATIONS IN NEURODYNAMICS[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 2036-2057. doi: 10.11948/20190321

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Chi Phan, Yuncheng You. EXPONENTIAL ATTRACTOR FOR HINDMARSH-ROSE EQUATIONS IN NEURODYNAMICS[J]. Journal of Applied Analysis & Computation, 2020, 10(5): 2036-2057. doi: 10.11948/20190321

EXPONENTIAL ATTRACTOR FOR HINDMARSH-ROSE EQUATIONS IN NEURODYNAMICS

Chi Phan^1, ,,
Yuncheng You^2, ,

1.
Department of Mathematics and Statistics, Sam Houston State University, Huntsville, TX 77340, USA
2.
Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

Corresponding authors: Email address: chp007@shsu.edu (C. Phan); Email address: you@mail.usf.edu (Y. You)

Abstract

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.
- Diffusive Hindmarsh-Rose equations /
- exponential attractor /
- squeezing property /
- compact absorbing set /
- finite fractal dimension

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References

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