On the covariance matrix of the stationary distribution of a noisy dynamical system
On the covariance matrix of the stationary distribution of a noisy dynamical system
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DOI：
10.1587/nolta.9.166
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Makito Oku;K. Aihara
中科院分区：
文献类型：
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作者：
Makito Oku;K. Aihara
本文分析了基于线性逼近的噪声动力系统的稳定性与其平稳分布的协方差矩阵之间的关系。我们用协方差矩阵重新表述了动态网络生物标记的理论，并阐明了协方差矩阵在动力系统接近分岔点时的极限行为。讨论了雅可比矩阵与主成分分析的关系。并给出了一个简单的非线性网络模型的应用。
In this paper, we analyze the relation between the stability of a noisy dynamical system based on linear approximation and the covariance matrix of its stationary distribution. We reformulate the theory of dynamical network biomarkers in terms of the covariance matrix and clarify the limiting behavior of the covariance matrix when a dynamical system approaches a bifurcation point. We also discuss the relation between the Jacobian matrix and principal component analysis. An application to a simple nonlinear network model is also demonstrated.