Volterra-series approach to stochastic nonlinear dynamics: The Duffing oscillator driven by white noise
Roman Belousov (@ribelousov), Florian Berger (@DrFlorianBerger), A. J. Hudspeth.
The Duffing oscillator is a classical model of bistable oscillatory motion in physics, engineering, and biology. However, reconstruction of the model’s parameter values from experimental observations of such oscillations in the presence of noise is one of the unsolved and challenging problems in physics of nonlinear systems. We develop non-traditional techniques for the analysis of bistable systems. Our approach yields new theoretical results on the statistics of the Duffing oscillator that directly address this deficiency and opens a new avenue for studying similar issues of nonlinear dynamics and statistical mechanics.