Properties of networks with partially structured and partially random connectivityAhmadian, Y., F. Fumarola and K.D. Miller (2013)Physical Review E 91:012820We provide a general formula for the eigenvalue density of large random N×N matrices of the form A=M+LJR, where M, L and R are arbitrary deterministic matrices and J is a random matrix of zero-mean independent and identically distributed elements. For A nonnormal, the eigenvalues do not suffice to specify the dynamics induced by A, so we also provide general formulae for the transient evolution of the magnitude of activity and frequency power spectrum in an N-dimensional linear dynamical system with a coupling matrix given by A. These quantities can also be thought of as characterizing the stability and the magnitude of the linear response of a nonlinear network to small…

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