The almost-sure asymptotic stability of a pair of coupled linear oscillators whose frequencies are equal or nearly equal and parametrically excited by a wideband stochastic process is investigated. Using the method of stochastic averaging and a Fourier expansion technique for solving the Fokker-Planck equation associated with the response angles, the maximal Lyapunov exponent is evaluated. The sign of the Lyapunov exponent determines the stability or instability of the oscillators. The cases when the frequency matrix is of diagonal form and of Jordan-canonical form are considered.
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