Li Yang, Shi Jifan, Aihara Kazuyuki
International Research Center for Neurointelligence (WPI-IRCN), The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan.
Chaos. 2022 Jun;32(6):063114. doi: 10.1063/5.0081295.
This paper presents analyses of networks composed of homogeneous Stuart-Landau oscillators with symmetric linear coupling and dynamical Gaussian noise. With a simple mean-field approximation, the original system is transformed into a surrogate system that describes uncorrelated oscillation/fluctuation modes of the original system. The steady-state probability distribution for these modes is described using an exponential family, and the dynamics of the system are mainly determined by the eigenvalue spectrum of the coupling matrix and the noise level. The variances of the modes can be expressed as functions of the eigenvalues and noise level, yielding the relation between the covariance matrix and the coupling matrix of the oscillators. With decreasing noise, the leading mode changes from fluctuation to oscillation, generating apparent synchrony of the coupled oscillators, and the condition for such a transition is derived. Finally, the approximate analyses are examined via numerical simulation of the oscillator networks with weak coupling to verify the utility of the approximation in outlining the basic properties of the considered coupled oscillator networks. These results are potentially useful for the modeling and analysis of indirectly measured data of neurodynamics, e.g., via functional magnetic resonance imaging and electroencephalography, as a counterpart of the frequently used Ising model.
本文介绍了由具有对称线性耦合和动态高斯噪声的均匀斯图尔特 - 朗道振荡器组成的网络分析。通过简单的平均场近似，将原始系统转换为一个替代系统，该替代系统描述了原始系统的不相关振荡/波动模式。使用指数族来描述这些模式的稳态概率分布，并且系统的动力学主要由耦合矩阵的特征值谱和噪声水平决定。模式的方差可以表示为特征值和噪声水平的函数，从而得出振荡器协方差矩阵与耦合矩阵之间的关系。随着噪声降低，主导模式从波动变为振荡，产生耦合振荡器的明显同步，并推导了这种转变的条件。最后，通过弱耦合振荡器网络的数值模拟来检验近似分析，以验证该近似在勾勒所考虑的耦合振荡器网络基本特性方面的效用。这些结果对于神经动力学间接测量数据的建模和分析可能是有用的，例如通过功能磁共振成像和脑电图，作为常用伊辛模型的对应物。
