Multi-headed loop chimera states in coupled oscillators

2021 ◽  
Vol 31 (1) ◽  
pp. 013135
Author(s):  
Dawid Dudkowski ◽  
Krzysztof Czołczyński ◽  
Tomasz Kapitaniak
Keyword(s):  
Coupled Oscillators ◽  
Chimera States

scholarly journals Mathematical Framework for Breathing Chimera States

2022 ◽  
Vol 32 (2) ◽  
Author(s):  
O. E. Omel’chenko
Keyword(s):  
Coupled Oscillators ◽  
Analytic Solution ◽  
Coarse Grained ◽  
Mathematical Framework ◽  
Intensive Study ◽  
Phase Oscillators ◽  
Chimera States ◽  
The Subject ◽  
Self Consistency

AbstractAbout 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.

scholarly journals Cascades of Multiheaded Chimera States for Coupled Phase Oscillators

2014 ◽  
Vol 24 (08) ◽  
pp. 1440014 ◽  
Author(s):  
Yuri L. Maistrenko ◽  
Anna Vasylenko ◽  
Oleksandr Sudakov ◽  
Roman Levchenko ◽  
Volodymyr L. Maistrenko
Keyword(s):  
Periodic Orbit ◽  
Coupled Oscillators ◽  
Phase Oscillators ◽  
Invariant Circle ◽  
Saddle Node Bifurcation ◽  
Chimera States ◽  
Chimera State ◽  
Self Organized ◽  
Saddle Node ◽  
Different Types

Chimera state is a recently discovered dynamical phenomenon in arrays of nonlocally coupled oscillators, that displays a self-organized spatial pattern of coexisting coherence and incoherence. We discuss the appearance of the chimera states in networks of phase oscillators with attractive and with repulsive interactions, i.e. when the coupling respectively favors synchronization or works against it. By systematically analyzing the dependence of the spatiotemporal dynamics on the level of coupling attractivity/repulsivity and the range of coupling, we uncover that different types of chimera states exist in wide domains of the parameter space as cascades of the states with increasing number of intervals of irregularity, so-called chimera's heads. We report three scenarios for the chimera birth: (1) via saddle-node bifurcation on a resonant invariant circle, also known as SNIC or SNIPER, (2) via blue-sky catastrophe, when two periodic orbits, stable and saddle, approach each other creating a saddle-node periodic orbit, and (3) via homoclinic transition with complex multistable dynamics including an "eight-like" limit cycle resulting eventually in a chimera state.

A SYSTEMATIC STUDY OF NONLOCALLY COUPLED OSCILLATORS AND CHIMERA STATES

2013 ◽  
Vol 27 (31) ◽  
pp. 1350180 ◽  
Author(s):  
LARRY LIN ◽  
PING-CHENG LI ◽  
HSENG-CHE TSENG
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Phase Portrait ◽  
Systematic Study ◽  
Coupled Oscillators ◽  
Nonlocal Parameter ◽  
Phase Lag ◽  
Space System ◽  
Chimera States ◽  
System Power

Oscillators under nonlocal couplings are systematically studied. We propose functions of inverse power as mathematical realization for nonlocal couplings among oscillators in a system. Power β in a function is taken as an important parameter in our study. Since its value determines a measure of "localization" while oscillators are nonlocally coupled it is then called the "nonlocal parameter". Together with the "phase lag parameter" α, which is vital for the existence of chimera states, we are able to demonstrate a valuable phase portrait in the β-α space. System dynamics is discussed in this phase diagram analogous to phase transitions in thermodynamics.

scholarly journals Chimera States for Coupled Oscillators

2004 ◽  
Vol 93 (17) ◽  
Author(s):  
Daniel M. Abrams ◽  
Steven H. Strogatz
Keyword(s):  
Coupled Oscillators ◽  
Chimera States

Interaction of chimera states in a multilayered network of nonlocally coupled oscillators

2017 ◽  
Vol 43 (8) ◽  
pp. 712-715 ◽  
Author(s):  
M. V. Goremyko ◽  
V. A. Maksimenko ◽  
V. V. Makarov ◽  
D. Ghosh ◽  
B. Bera ◽  
...  
Keyword(s):  
Coupled Oscillators ◽  
Chimera States

scholarly journals Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators

Nonlinearity ◽  
2015 ◽  
Vol 28 (3) ◽  
pp. R67-R87 ◽  
Author(s):  
Mark J Panaggio ◽  
Daniel M Abrams
Keyword(s):  
Coupled Oscillators ◽  
Chimera States

scholarly journals Between synchrony and turbulence: intricate hierarchies of coexistence patterns

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Sindre W. Haugland ◽  
Anton Tosolini ◽  
Katharina Krischer
Keyword(s):  
Phase Space ◽  
Coupled Oscillators ◽  
High Dimensional ◽  
Chimera States ◽  
Wide Range ◽  
One Step ◽  
Different Parts

AbstractCoupled oscillators, even identical ones, display a wide range of behaviours, among them synchrony and incoherence. The 2002 discovery of so-called chimera states, states of coexisting synchronized and unsynchronized oscillators, provided a possible link between the two and definitely showed that different parts of the same ensemble can sustain qualitatively different forms of motion. Here, we demonstrate that globally coupled identical oscillators can express a range of coexistence patterns more comprehensive than chimeras. A hierarchy of such states evolves from the fully synchronized solution in a series of cluster-splittings. At the far end of this hierarchy, the states further collide with their own mirror-images in phase space – rendering the motion chaotic, destroying some of the clusters and thereby producing even more intricate coexistence patterns. A sequence of such attractor collisions can ultimately lead to full incoherence of only single asynchronous oscillators. Chimera states, with one large synchronized cluster and else only single oscillators, are found to be just one step in this transition from low- to high-dimensional dynamics.

Multicluster and traveling chimera states in nonlocal phase-coupled oscillators

2014 ◽  
Vol 90 (2) ◽  
Author(s):  
Jianbo Xie ◽  
Edgar Knobloch ◽  
Hsien-Ching Kao
Keyword(s):  
Coupled Oscillators ◽  
Chimera States
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