Numerical simulation for a Duffing oscillator driven by white noise with constant and time-varying noise strengths

Abstract

We present a numerical analysis of the Duffing oscillator driven by white noise with constant and sinusoidally varying noise strengths. For each ‘noise strength history’ the Runge-Kutta method was used to generate trajectories corresponding to 200 to 500 realizations of the noise for the driven Duffing oscillator. The plot of variance versus time was obtained and analyzed. The results obtained for 200, 300, 400, and 500 realizations were in good agreement. It is observed that for both the constant noise strength and sinusoidal noise strength cases the variance exhibits a generally increasing trend but with an additional oscillatory fluctuation. However the nature of the oscillatory fluctuation is different for the two cases. For the constant noise strength case the amplitude of the oscillatory fluctuation is increasing; while for the case with sinusoidal noise strength the amplitude of the oscillatory fluctuation is modulated. The variance is generally larger for noise strength that oscillates with a frequency ω = 1.32 than for ω = 100 and ω = 0.01.