Deformation of nonequilibrium limit cycle oscillators due to stochasticity

Non-equilibrium dynamics are exhibited by numerous biological systems, often modeled as non-linear oscillations driven by an internal energy-consuming process. Thermal processes lead to stochasticity in the measurements of their variables. Thus, experiments can only access the mean limit cycle, which may be different from the underlying zero-temperature one. This can lead to discrepancies between measurements and deterministic numerical models.

One example of an active oscillator is the inner ear hair cell. Its dynamics are here modeled with a set of equations that incorporates the physiological variables and their noise amplitudes. We observe a gradual rounding of the mean limit cycle with increasing noise strength and explore causes for such rounding that makes sharper features of the noiseless oscillator experimentally inaccessible.

To simplify the system, we simulate a generalized Hopf oscillator, with added features in the scalar potential. The oscillation, powered by an internal active mechanism, requires a nonzero vector potential. By varying noise strengths under such general conditions, we observe distortion of the zero-temperature limit cycle. We suggest that this temperature effect imposes inherent limitations on complex models seeking to reproduce experimental dynamics.