Nonequilibrium limit-cycle oscillators: Fluctuations in hair bundle dynamics

Area of Science:

• Nonlinear dynamics
• Statistical physics
• Biophysics

Background:

• Quasiperiodic dynamics and limit cycle oscillators are prevalent in nonequilibrium systems.
• Spontaneous oscillations in biological systems, such as inner ear hair cells, exemplify these dynamics.

Purpose of the Study:

• To develop a general framework for interpreting stochastic dynamical systems near a limit cycle.
• To analyze the effects of noise on limit cycle oscillators.
• To apply the framework to biological systems.

Main Methods:

• Development of a theoretical framework for stochastic dynamical systems.
• Analysis of phase diffusion and orthogonal deviations in the presence of noise.
• Investigation of frequency dependence mechanisms and temperature-dependent limit cycle deformation.

Main Results:

• Noise causes phase diffusion in limit cycle oscillators.
• Orthogonal deviations exhibit a Lorentzian power spectrum characteristic of damped oscillators.
• Two mechanisms for complex frequency dependence were identified.
• The mean limit cycle deformation was analyzed as a function of temperature.

Conclusions:

• The developed framework provides a general interpretation of stochastic dynamics near limit cycles.
• The findings offer insights into the behavior of noisy oscillators in physical and biological systems.
• The study successfully applied theoretical concepts to experimental data from hair cells.