Detecting Limit Cycles in Stochastic Time Series

The emergence of oscillatory behaviour represents fundamental information about the interactions of the underlying system. In biological systems, oscillations have been observed in experimental data, but due to the significant level of noise, it is difficult to characterize whether observed dynamics based on time series, are truly limit cycles. Here, we present a simple three step method to identify the presence of limit cycles in stochastic systems. Considering input from one-dimensional time series, as are typically obtained in experiments, we show statistical measures to detect the existence of limit cycles. This is tested on models from chemical networks, and we investigate how the underlying dynamics can be separated depending on the noise level and length of the series