Role of additive gaussian noise in suppressing chaos by weak harmonic excitations

Abstract

The effect of additive Gaussian noise on the chaos-suppression scenario of a broad and important family of dissipative nonautonomous systems subjected to chaos-suppressing excitations is investigated by means of Melnikov's method. The analysis indicates that the optimal suppressory initial phase differences between the chaos-inducing and chaos suppressing forcing terms remain the same as in the purely deterministic case, while the ranges of suppressory initial phase differences and amplitudes narrow as noise strenght is increased from zero. Computer simulations of a two-well Duffing oscillator confirm the theoretical predictions.