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Deriving meaningful information from observational data is often restrictedby many limiting factors, the most important of which is the presence of noise.In this work, we present the use of the bicoherence function to extractinformation about the underlying nonlinearity from noisy time series. We showthat a system evolving in the presence of noise which has its dynamical stateconcealed from quantifiers like the power spectrum and correlation dimensionD2, can be revealed using the bicoherence function. We define an index calledmain peak bicoherence function as the bicoherence associated with the maximalpower spectral peak. We show that this index is extremely useful while dealingwith quasi-periodic data as it can distinguish strange non chaos from quasiperiodicity even with added noise. We demonstrate this in a real worldscenario, by taking the bicoherence of variable stars showing period doublingand strange non-chaotic behavior. Our results indicate that bicoherenceanalysis can also bypass the method of surrogate analysis using Fourier phaserandomization, used to differentiate linear stochastic processes from nonlinear ones, in conventional methods involving measures like D2.

Detecting Dynamical States from Noisy Time Series using Bicoherence