Synchronization of Boundary Coupled Hindmarsh-Rose Neuron Network
Chi Phan, Yuncheng You
TL;DR
This paper introduces a mathematical model of boundary coupled Hindmarsh-Rose neuron networks, proving conditions for their exponential synchronization based on coupling strength and stimuli.
Contribution
It establishes the global absorbing property and synchronization conditions for a new boundary coupled neuron network model.
Findings
Global absorbing property proved
Exponential synchronization achieved under certain thresholds
Synchronization rate quantified
Abstract
In this work, we present a new mathematical model of a boundary coupled neuron network described by the partly diffusive Hindmarsh-Rose equations. We prove the global absorbing property of the solution semiflow and then the main result on the asymptotic synchronization of this neuron network at a uniform exponential rate provided that the boundary coupling strength and the stimulating signal exceed a quantified threshold in terms of the parameters.
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Taxonomy
Topicsstochastic dynamics and bifurcation · Nonlinear Dynamics and Pattern Formation · Neural Networks Stability and Synchronization