In this paper, the evolutionary behavior of the transfer matrix element moments in strongly coupled multimode systems is studied analytically. The randomly coupled multimode system is modeled by a set of coupled stochastic differential equations (SDEs), which can be used to find the coupled ordinary differential equations (ODEs) for the arbitrary order moments of the matrix elements. Since the ODEs are with the constant coefficients, it is possible to obtain the analytical solutions. The asymptotic behaviors of the solutions are investigated by comparing with the existing results derived from the property of the Haar matrix, and a perfect agreement is observed. The evolutionary behaviors of the transfer matrix element moments computed by the analytical formulas have excellent match with the Monte Carlo simulation results. The analytical method can be highly beneficiary for the multimode system design and analysis.
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