Dynamics and Synchronization of Boundary Coupled FitzHugh-Nagumo Neural Networks

2020/05/07 by Lesław Skrzypek, Skrzypek, Leslaw, Yuncheng You +1
Computer Science · Neuroscience · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.2005.05394

openalex publication_date 2020/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work a new mathematical model for complex neural networks is presented by the partly diffusive FitzHugh-Nagumo equations with ensemble boundary coupling. We analyze the dissipative dynamics and boundary coupling dynamics of the solution semiflow with sharp estimates. The exponential synchronization of this kind complex neural networks is proved under the condition that synaptic stimulation signal strength reaches a threshold quantitatively expressed.

Citations

• Impulses and Physiological States in Theoretical Models of Nerve Membrane
• Clamping and Synchronization in the strongly coupled FitzHugh-Nagumo\n model

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