Dynamics and synchronization of boundary coupled FitzHugh-Nagumo neural networks

In this work a new mathematical model for complex neural networks is presented by the partly diffusive FitzHugh-Nagumo equations with ensemble boundary coupling. The dissipative dynamics and boundary coupling dynamics of solutions are proved with sharp uniform estimates. The synchronization of this kind complex neural networks is proved under the condition that boundary synaptic stimulation signal strength exceeds the threshold quantitatively expressed. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

A new mathematical model for complex neural networks is proposed in this work, using the partly diffusive FitzHugh-Nagumo equations with ensemble boundary coupling to achieve synchronization. The dissipative dynamics and boundary coupling dynamics are proven with sharp uniform estimates, and synchronization is demonstrated under specific conditions regarding the strength of boundary synaptic stimulation signals.