Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise

Abstract

We discuss control techniques for noisy self-sustained oscillators with a focus on reliability, stability of the response to noisy driving, and oscillation coherence understood in the sense of constancy of oscillation frequency. For any kind of linear feedback control--single and multiple delay feedback, linear frequency filter, etc.--the phase diffusion constant, quantifying coherence, and the Lyapunov exponent, quantifying reliability, can be efficiently controlled but their ratio remains constant. Thus, an "uncertainty principle" can be formulated: the loss of reliability occurs when coherence is enhanced and, vice versa, coherence is weakened when reliability is enhanced. Treatment of this principle for ensembles of oscillators synchronized by common noise or global coupling reveals a substantial difference between the cases of slightly non-identical oscillators and identical ones with intrinsic noise.

10 pages, 5 figures

References in corpus (6)

• Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators
• Dynamics of Limit Cycle Oscillator Subject to General Noise
• Are generalized synchronization and noise--induced synchronization identical types of synchronous behavior of chaotic oscillators?
• Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses
• Anharmonic resonances with recursive delay feedback
• Synchronization of Limit Cycle Oscillators by Telegraph Noise

Cited by in corpus (4)

• Anharmonic resonances with recursive delay feedback
• Circular Cumulant Reductions for Macroscopic Dynamics of Kuramoto Ensemble with Multiplicative Intrinsic Noise
• Synchronization in Kuramoto-Sakaguchi ensembles with competing influence of common noise and global coupling
• Coherence of Noisy Oscillators with Delayed Feedback Inducing Multistability