Maximizing coherence of oscillations by external locking

TL;DR

This paper investigates how external locking can be used to maximize the coherence of noisy oscillations, deriving optimal forcing strategies in different noise regimes and analyzing their bifurcations.

Contribution

It provides explicit formulas for optimal forcing to enhance oscillator coherence, considering both small and large noise limits, and compares with deterministic locking conditions.

Findings

Optimal forcing minimizes phase diffusion constant.

Optimal force form bifurcates with noise intensity.

Results connect stochastic and deterministic locking conditions.

Abstract

We study how the coherence of noisy oscillations can be optimally enhanced by external locking. Basing on the condition of minimizing the phase diffusion constant, we find the optimal forcing explicitly in the limits of small and large noise, in dependence of phase sensitivity of the oscillator. We show that the form of the optimal force bifurcates with the noise intensity. In the limit of small noise, the results are compared with purely deterministic conditions of optimal locking.