Response of nonlinear oscillators with random frequency of excitation, revisited

Periodically driven oscillators of low-frequency random excitations are analyzed. Computer simulation, which was carried out for the Duffing equation and forced vibrations of a pendulum, indicated that in these cases noise has a stabilizing effect. Computation of Lyapunov exponents showed that by adding noise to chaotic motion the largest Lyapunov exponent as a rule turns to negative and, consequently, the chaotic motion is annihilated.