Computer Simulation of Noise Effects of the Neighborhood of Stimulus Threshold for a Mathematical Model of Homeostatic Regulation of Sleep-Wake Cycles

Wuyin Jin,An Wang,Chunni Wang,Qian Lin

doi:10.1155/2017/4797545

Abstract

The noise effects on a homeostatic regulation of sleep-wake cycles’ neuronal mathematical model determined by the hypocretin/orexin and the local glutamate interneurons spatiotemporal behaviors are studied within the neighborhood of stimulus threshold in this work; the neuronal noise added to the stimulus, the conductance, and the activation variable of the modulation function are investigated, respectively, based on a circadian input skewed in sine function. The computer simulation results suggested that the increased amplitude of external current input will lead to the fact that awakening time is advanced but the sleepy time remains the same; for the bigger conductance and modulation noise, the regulatory mechanism of the model sometimes will be collapsed and the coupled two neurons of the model show very irregular activities; the falling asleep or wake transform appears at nondeterminate time.

Highlights

Noise is a problem for neurons, and can be a solution in information processing
Neural noise is a general term that designates random influences on the transmembrane voltage of single neurons and by extension of the firing activity of neural networks. This noise can influence the transmission and integration of signals from other neurons and alter the firing activity of neurons in isolation [2,3,4], and there are some significant effects near bifurcation points [5, 6], the weak neural noise, that seem to be less relevant when the neurons operate in spike generating regime for a suprathreshold; the situation is completely different in the neighborhood of threshold where noise can induce significant changes in the impulse patterns; in the central neural system, the neurons often work in the neighborhood of threshold, but neurons are heterogeneous and noise is inevitable [7]
Complexity between connection neurons [14, 15]; in this work, we study the spatiotemporal behaviors of noise effects in the neighborhood of stimulus threshold for a mathematical model of homeostatic regulation of sleep-wake cycles proposed by Postnova et al [16]

Summary

Introduction

Noise is a problem for neurons, and can be a solution in information processing. Neural noise is a general term that designates random influences on the transmembrane voltage of single neurons and by extension of the firing activity of neural networks This noise can influence the transmission and integration of signals from other neurons and alter the firing activity of neurons in isolation [2,3,4], and there are some significant effects near bifurcation points [5, 6], the weak neural noise, that seem to be less relevant when the neurons operate in spike generating regime for a suprathreshold; the situation is completely different in the neighborhood of threshold where noise can induce significant changes in the impulse patterns; in the central neural system, the neurons often work in the neighborhood of threshold, but neurons are heterogeneous and noise is inevitable [7]. The effects of neuronal noise added to the stimulus, the conductance, and the modulation function are investigated, respectively, based on a circadian input skewed in sine function proposed by Daan et al [17]

Model and Input dV

Regulation of Sleep-Wake Cycles of the Deterministic

Conclusions