2022/08/11 by Yuncheng You, You, Yuncheng · 1 citation
Computer Science · Medicine · Physics and Astronomy · #35B40 #35B41 #35K55 #35Q92 #92C20 #Analysis of PDEs (math.AP) #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Neurons and Cognition (q-bio.NC) #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2208.06012
openalex publication_date 2022/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Global dynamics of the diffusive Hindmarsh-Rose equations with memristor as a new proposed model for neuron dynamics are investigated in this paper. We prove the existence and regularity of a global attractor for the solution semiflow through uniform analytic estimates showing the higher-order dissipative property and the asymptotically compact characteristics of the solution semiflow by the approach of Kolmogorov-Riesz theorem. The quantitative bounds of the regions containing this global attractor respectively in the state space and in the regular space are explicitly expressed by the model parameters.