Dynamics and Synchronization of Boundary Coupled FitzHugh-Nagumo Neural Networks

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.

Feedback Synchronization of FHN Cellular Neural Networks

“…Recently we proved results on the exponential synchronization of the boundary coupled Hindmarsh-Rose neural networks in [15,16] and the boundary coupled partly diffusive FitzHugh-Nagumo neural networks in [19].…”

“…In this work, we consider a CNN model as the discrete replacement of the biological neural networks described by the partial diffusive FitzHugh-Nagumo equations with different coupling patterns [11,19,20,23,24],…”