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Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

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Published on: September 21, 2017

Coherence versus reliability of stochastic oscillators with delayed feedback.

Denis S Goldobin¹

¹Department of Theoretical Physics, Perm State University, 15 Bukireva street, 614990 Perm, Russia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 5, 2009

Summary

Researchers found a quantitative link between coherence and reliability in noisy oscillators. This discovery, important for applications like neurons and lasers, was previously unexamined, offering new control insights.

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Area of Science:

Nonlinear dynamics
Complex systems
Oscillator theory

Background:

Noisy self-sustained oscillators are crucial in various fields, including neuroscience, photonics, and power generation.
Reliability (response stability) and coherence (frequency stability) are key performance metrics for these oscillators.
These critical characteristics have traditionally been studied in isolation, limiting a holistic understanding of oscillator behavior.

Purpose of the Study:

To investigate the relationship between coherence and reliability in limit cycle oscillators under noisy conditions.
To explore the impact of linear delayed feedback as a control mechanism on these characteristics.
To establish a quantitative connection between oscillator coherence and reliability.

Main Methods:

Analytical derivation of the relationship between coherence and reliability for a specific oscillator model.
Application of weak noisy driving and linear delayed feedback to the oscillator system.
Numerical simulations using the Van der Pol-Duffing oscillator to validate analytical findings.

Main Results:

A strong quantitative relationship between coherence and reliability was established for the first time.
Linear delayed feedback was identified as an effective tool for controlling both coherence and reliability.
Analytical findings were confirmed and expanded through numerical simulations.

Conclusions:

Coherence and reliability in noisy oscillators are intrinsically linked and can be controlled simultaneously.
The study provides a novel framework for understanding and optimizing oscillator performance in the presence of noise.
This research has significant implications for designing more robust and stable systems in neuroscience, engineering, and physics.