Dynamics and synchronization of boundary coupled FitzHugh-Nagumo neural networks

摘要

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.