Open AccessThird party stabilization of unstable coordination in systems of coupled oscillators
Author(s) -
Joseph McKinley,
Mengsen Zhang,
Alice Wead,
Christine L. Williams,
Emmanuelle Tognoli,
Christopher Beetle
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2090/1/012167
Subject(s) - bistability , generalization , coupling (piping) , adaptability , computer science , microscale chemistry , flexibility (engineering) , complex system , neural system , dynamical systems theory , property (philosophy) , van der pol oscillator , statistical physics , topology (electrical circuits) , artificial intelligence , nonlinear system , physics , mathematics , psychology , neuroscience , engineering , epistemology , quantum mechanics , mechanical engineering , mathematical analysis , biology , ecology , philosophy , statistics , mathematics education , combinatorics
The Haken-Kelso-Bunz (HKB) system of equations is a well-developed model for dyadic rhythmic coordination in biological systems. It captures ubiquitous empirical observations of bistability – the coexistence of in-phase and antiphase motion – in neural, behavioral, and social coordination. Recent work by Zhang and colleagues has generalized HKB to many oscillators to account for new empirical phenomena observed in multiagent interaction. Utilising this generalization, the present work examines how the coordination dynamics of a pair of oscillators can be augmented by virtue of their coupling to a third oscillator. We show that stable antiphase coordination emerges in pairs of oscillators even when their coupling parameters would have prohibited such coordination in their dyadic relation. We envision two lines of application for this theoretical work. In the social sciences, our model points toward the development of intervention strategies to support coordination behavior in heterogeneous groups (for instance in gerontology, when younger and older individuals interact). In neuroscience, our model will advance our understanding of how the direct functional connection of mesoscale or microscale neural ensembles might be switched by their changing coupling to other neural ensembles. Our findings illuminate a crucial property of complex systems: how the whole is different than the system’s parts.