Optimal phase-selective entrainment of heterogeneous oscillator ensembles

We develop a framework to design optimal entrainment signals that entrain an ensemble of heterogeneous nonlinear oscillators, described by phase models, at desired phases. We explicitly take into account heterogeneity in both oscillation frequency and the type of oscillators characterized by differe...

Full description

Saved in:
Bibliographic Details
Published inSIAM journal on applied dynamical systems Vol. 22; no. 3; p. 2180
Main Authors Singhal, Bharat, Kiss, István Z, Li, Jr-Shin
Format Journal Article
LanguageEnglish
Published United States 01.01.2023
Subjects
34C15
Phase model
37N35
37N25
92B25
Entrainment
Synchronization
34C29
Oscillators
Online AccessGet more information
ISSN1536-0040
1536-0040
DOI10.1137/22m1521201

Cover

More Information
Summary:We develop a framework to design optimal entrainment signals that entrain an ensemble of heterogeneous nonlinear oscillators, described by phase models, at desired phases. We explicitly take into account heterogeneity in both oscillation frequency and the type of oscillators characterized by different Phase Response Curves. The central idea is to leverage the Fourier series representation of periodic functions to decode a phase-selective entrainment task into a quadratic program. We demonstrate our approach using a variety of phase models, where we entrain the oscillators into distinct phase patterns. Also, we show how the generalizability gained from our formulation enables us to meet a wide range of design objectives and constraints, such as minimum-power, fast entrainment, and charge-balanced controls.
ISSN:1536-0040
1536-0040
DOI:10.1137/22m1521201