Stochastic Resonance in the Duffing Oscillator with MATLAB

Compute and plot SNR vs. noise strength for the double-well Duffing oscillator.

Numerically solve the driven, damped, duffing oscillator with noise.

It computes the averaged signal and noise amplitude spectra for varying noise strength. Plots the signal-to-noise ratio vs. noise strength and time-series, phase space, well occupation distributions, and amplitude spectra for four chosen noise strengths.

Instead of modeling the random noise so that the differential equation is stochastic, the noise is treated analytically as a finite Fourier series, where the frequency and phase are random, and the noise type depends on the frequency dependent amplitude function.

This is not the most efficient way numerically, but allows one to calculate analytic results.

Can be easily modified for any second-order differential equation.