Global attractor of complex networks of reaction-diffusion systems of Fitzhugh-Nagumo type

B. Ambrosio; M. A. Aziz-Alaoui; V. L. E. Phan

doi:10.3934/dcdsb.2018077

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2018, Volume 23, Issue 9: 3787-3797. Doi: 10.3934/dcdsb.2018077

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Global attractor of complex networks of reaction-diffusion systems of Fitzhugh-Nagumo type

1.
Normandie Univ, UNIHAVRE, LMAH, FR-CNRS-3335, ISCN, 76600 Le Havre, France
2.
Normandie Univ, France
3.
An Giang University, Long Xuyen City, Vietnam

* Corresponding author
* Corresponding author

Received: April 30, 2016

Revised: October 31, 2017

Early access: March 2018

Published: September 2018

This research was funded by Region Normandie France and the ERDF (European Regional Development Fund) project XTERM.

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Abstract

We focus on the long time behavior of complex networks of reaction-diffusion systems. We prove the existence of the global attractor and the $L^{∞}$-bound for networks of $n$ reaction-diffusion systems that belong to a class that generalizes the FitzHugh-Nagumo reaction-diffusion equations.

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Mathematics Subject Classification: 35B40, 35B41, 35K57.

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