高斯色噪声对耦合神经元的放电模式和相位同步的影响

Effect of Gaussian Color Noise on Firing Mode and Phase Synchronization of Coupled Neurons

摘要: 大脑中的神经系统是由众多的神经元所构成，神经元的放电模式与相位同步在不同的条件下表现出不一样的动力学行为。本文首先建立了具有高斯色噪声和时间延迟的耦合神经元模型，并从理论上推导了在时间延迟存在的情况下耦合神经元的同步流形，然后以高斯色噪声为研究对象，探究了与高斯色噪声有关的一些参量(包括耦合神经元之间的相互关联度、耦合强度、噪声强度、时间延迟的大小)对耦合神经元放电模式与相位同步的作用与影响。结果表明：在固定的单时延背景下，噪声强度和相互关联度都是通过改变神经元放电所产生的峰之间的间隔来影响神经元的放电模式的，从总体上来说，连续增大噪声强度和相互关联度会使峰峰间隔呈相似规律地减小；耦合强度是通过改变神经元放电过程中的局部峰值来影响神经元的放电模式的，耦合强度越大，神经元放电过程中出现的不同局部峰值越多。在双时延和双耦合的背景下，相互关联度和噪声强度从较小值逐渐增大的过程中，耦合神经元的相位变化情况都是交替的同步和异步状态→异步状态→相位漂移和反相位状态的共存或交替；双时延的差值从零逐渐增大的过程中，耦合神经元的相位变化情况是：异步状态→相位漂移和反相位状态共存或交替→相位漂移状态；双耦合强度的差值从较小值逐渐增大的过程中，耦合神经元始终处于相位漂移状态，但是其整体的相位同步性会增强。

Abstract: The nervous system in the brain is composed of numerous neurons, and the firing patterns and phase synchronization of neurons show different kinetic behaviors under different conditions. In this paper, we firstly establish a coupled neuron model with Gaussian color noise and time delay, and theoretically derive the synchronization flow pattern of coupled neurons in the presence of time delay. And then we take Gaussian colored noise as the research object to investigate the role and influence of some parameters related to Gaussian colored noise on the firing pattern and phase synchronization of coupled neurons. The results show that in a fixed single time delay background, both noise intensity and intercorrelation affect the firing pattern of neurons by changing the interval between the peaks generated by neuronal discharge, and in general, increasing noise intensity and intercorrelation continuously decreases the interval between peaks in a similar pattern; coupling intensity affects the firing pattern of neurons by changing the local peaks during neuronal discharge. The greater the coupling strength, the more different local peaks appear during the neuron discharge. In the context of double time delay and double coupling, the phase change of the coupled neuron is alternately synchronous and asynchronous → asynchronous → coexistence or alternation of phase drift and anti-phase states during the gradual increase of intercorrelation and noise intensity from smaller values; the phase change of the coupled neuron is: asynchronous → phase drift and anti-phase states during the gradual increase of the difference of double time delay from zero coexistence or alternation → phase drift state; during the process of gradually increasing the difference of dual coupling strength from smaller values, the coupled neuron is always in phase drift state, but its overall phase synchronization will be enhanced.