Multi-pulse phase resetting curve

TL;DR

This paper investigates how dual pulse excitations affect autonomous oscillators, revealing non-linear deviations from linear superposition in phase response curves, with implications for modeling and analyzing pulse-coupled networks.

Contribution

It introduces a systematic study of dual pulse effects on oscillators using phase response curves and derives a correction term for higher-dimensional models.

Findings

Non-linear correction proportional to the square of the perturbation.

Deviations from superposition principle are significant in higher-dimensional oscillators.

The correction term can be used to verify oscillator models.

Abstract

In this paper, we introduce and systematically study, in terms of phase response curves (PRC), the effect of a dual pulse excitation on the dynamics of an autonomous oscillator. Specifically, we test the deviations from a linear summation of phase advances from two small perturbations. We derive analytically a correction term, which generally appears for oscillators whose intrinsic dimensionality is greater than one. We demonstrate this effect in case of the Stuart-Landau model, and also in various higher dimensional neuronal model. The non-linear correction is found to be proportional to the square of the perturbation. This deviation from the superposition principle needs to be taken into account in studies of networks of pulse-coupled oscillators. Further, this deviation could be used for verification of oscillator models via a dual pulse excitation.