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On the covariance matrix of the stationary distribution of a noisy dynamical system
Makito Oku (University of Toyama, Institute of Natural Medicine, University of Toyama), Kazuyuki Aihara (Institute of Industrial Science, The University of Tokyo, The University of Tokyo)
Abstract: 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.