  Deriving meaningful information from observational data is often restricted
by 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 extract
information about the underlying nonlinearity from noisy time series. We show
that a system evolving in the presence of noise which has its dynamical state
concealed from quantifiers like the power spectrum and correlation dimension
D2, can be revealed using the bicoherence function. We define an index called
main peak bicoherence function as the bicoherence associated with the maximal
power spectral peak. We show that this index is extremely useful while dealing
with quasi-periodic data as it can distinguish strange non chaos from quasi
periodicity even with added noise. We demonstrate this in a real world
scenario, by taking the bicoherence of variable stars showing period doubling
and strange non-chaotic behavior. Our results indicate that bicoherence
analysis can also bypass the method of surrogate analysis using Fourier phase
randomization, used to differentiate linear stochastic processes from non
linear ones, in conventional methods involving measures like D2.
