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  • 1Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 24/25, 14476 Potsdam-Golm, Germany and Department of Control Theory, Nizhni Novgorod State University, Gagarin Avenue 23, 606950 Nizhni Novgorod, Russia.

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We found the best way to improve noisy oscillations using external locking by minimizing phase diffusion. The optimal forcing strategy changes with noise intensity and oscillator sensitivity.

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Area of Science:

  • Nonlinear dynamics
  • Stochastic processes
  • Biophysics

Background:

  • Noisy oscillations are common in natural systems.
  • External locking can control oscillatory behavior.
  • Optimizing this control is crucial for enhancing coherence.

Purpose of the Study:

  • To determine the optimal external forcing for enhancing coherence in noisy oscillations.
  • To analyze how optimal forcing depends on noise intensity and oscillator properties.
  • To investigate the transition in optimal forcing strategies.

Main Methods:

  • Minimizing the phase diffusion constant to find optimal forcing.
  • Analytical calculations in the limits of small and large noise.
  • Comparison with experimental data from neural cells.

Main Results:

  • Explicit formulas for optimal forcing were derived for different noise levels.
  • The optimal forcing strategy bifurcates with increasing noise intensity.
  • Experimental validation using neural cell phase sensitivity was performed.

Conclusions:

  • Optimal external locking strategies for noisy oscillations are noise-dependent.
  • A transition in optimal forcing occurs with varying noise intensity.
  • The findings have implications for controlling biological and physical oscillators.