Paper Info
Title
Mathematical Framework for Breathing Chimera States
Abstract
About two decades ago it was discovered that systems of nonlocally coupled oscillators can exhibit unusual symmetry-breaking patterns composed of coherent and incoherent regions. Since then such patterns, called chimera states, have been the subject of intensive study but mostly in the stationary case when the coarse-grained system dynamics remains unchanged over time. Nonstationary coherence-incoherence patterns, in particular periodically breathing chimera states, were also reported, however not investigated systematically because of their complexity. In this paper we suggest a semi-analytic solution to the above problem providing a mathematical framework for the analysis of breathing chimera states in a ring of nonlocally coupled phase oscillators. Our approach relies on the consideration of an integro-differential equation describing the long-term coarse-grained dynamics of the oscillator system. For this equation we specify a class of solutions relevant to breathing chimera states. We derive a self-consistency equation for these solutions and carry out their stability analysis. We show that our approach correctly predicts macroscopic features of breathing chimera states. Moreover, we point out its potential application to other models which can be studied using the Ott-Antonsen reduction technique.
Year
DOI
Venue
2022
10.1007/s00332-021-09779-1
JOURNAL OF NONLINEAR SCIENCE
Keywords
DocType
Volume
Coupled oscillators, Breathing chimera states, Coherence-incoherence patterns, Ott-Antonsen equation, Periodic solutions, Stability
Journal
32
Issue
ISSN
Citations 
2
0938-8974
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Oleh Omel'chenko100.34