Dynamics of Partial Differential Equations
Volume 18 (2021)
Global dynamics of partly diffusive Hindmarsh–Rose equations in neurodynamics
Pages: 33 – 47
Global dynamics of the partly diffusive Hindmarsh–Rose equations as a new mathematical model in neurodynamics is presented and studied in this paper. The existence of global attractor for the solution semiflow is proved through uniform estimates showing the higher-order dissipative property and the ultimate compactness by the new approach of Kolmogorov–Riesz theorem.
diffusive Hindmarsh–Rose equations, neurodynamics, global attractor, absorbing property, ultimate compactness, Kolmogorov–Riesz theorem
2010 Mathematics Subject Classification
35B41, 35K58, 35Q92, 37N25, 92C20
Jianzhong Su is partially supported by USDA Grant number 2018-38422-28564.
Received 15 June 2020
Published 19 February 2021