Telegraph Processes with Extrinsic Fluctuations: Burst Dynamics and an Application to Domestic Cat Activity

RESUMO

Animal activity often consists of intermittent bursts separated by prolonged periods of inactivity. Here, we describe this behavior using a two-state telegraph process with extrinsically fluctuating transition rates. We derived analytical expressions for the stationary behavior of the system and characterized how stationary fluctuations in the effective transition rates modified the activity and residence time statistics. In particular, we show that whereas fixed transition rates lead to exponential residence-time distributions, stationary rate fluctuations generate effective Lomax distributions with heavier tails. We also found that fluctuations can either increase or decrease the mean occupancy of the active state, and that when the fluctuations in the two transition rates are equal, their effect on the stationary occupancy becomes indistinguishable from the case without fluctuations. We assessed the parameter inference using synthetic data and applied the framework to observations of a domestic cat. For synthetic data, accounting for extrinsic fluctuations substantially improved the recovery of the kinetic parameters used to generate the data. In the experimental data, the inferred variability of the inactive-to-active transition rate was substantially larger than that of the active-to-inactive rate. These results establish a tractable framework for studying stochastic switching systems in which extrinsic variability reshapes burst and residence-time statistics.