Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems

TL;DR

This paper introduces a sensitivity analysis method for phase-response curves in oscillator models, providing new tools to analyze nonlinear systems like biological cellular rhythms.

Contribution

It develops theoretical and numerical tools for sensitivity analysis of phase-response curves, enhancing understanding of oscillator models as open systems.

Findings

New sensitivity analysis methods for phase-response curves

Application to biological cellular rhythm models

Insights into oscillator system properties

Abstract

Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for phase-response curves, a fundamental one-dimensional phase reduction of oscillator models. The proposed theoretical and numerical analysis tools are illustrated on several system-theoretic questions and models arising in the biology of cellular rhythms.