Many biological time series appear nonlinear or chaotic, and from biomechanical principles we can explain these empirical observations. For this reason, methods from nonlinear time series analysis have become important tools to characterise these systems. Nonetheless, a very large proportion of these signals appear to contain significant noise. This randomness cannot be explained within the assumptions of pure deterministic nonlinearity, and, as such, is often treated as a nuisance to be ignored or otherwise mitigated. However, recent work points to this noise component containing valuable information. Random dynamical systems offer a unified framework within which to understand the interplay between deterministic and stochastic dynamical sources. This talk will discuss recent attempts to exploit this synthesis of stochastic and deterministic dynamics in biological signals. It will include a case study from speech science.