Optimal phase response curves for stochastic synchronization of limit-cycle oscillators by common Poisson noise

TL;DR

This paper investigates how to optimize phase response curves to enhance stochastic synchronization of limit-cycle oscillators using common Poisson noise, revealing shape transitions from sinusoidal to sawtooth.

Contribution

It derives the optimal phase response curve shape by solving the Euler-Lagrange equation, showing how it varies with signal strength constraints.

Findings

Optimal shape is sinusoidal for weak signals.

Shape transitions from sinusoid to sawtooth with increased amplitude constraints.

Provides a mathematical framework for designing synchronization signals.

Abstract

We consider optimization of phase response curves for stochastic synchronization of non-interacting limit-cycle oscillators by common Poisson impulsive signals. The optimal functional shape for sufficiently weak signals is sinusoidal, but can differ for stronger signals. By solving the Euler-Lagrange equation associated with the minimization of the Lyapunov exponent characterizing synchronization efficiency, the optimal phase response curve is obtained. We show that the optimal shape mutates from a sinusoid to a sawtooth as the constraint on its squared amplitude is varied.