# Mathematical Framework for Breathing Chimera States

@article{Omelchenko2022MathematicalFF, title={Mathematical Framework for Breathing Chimera States}, author={Oleh E. Omel'chenko}, journal={Journal of Nonlinear Science}, year={2022}, volume={32}, pages={1-34} }

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…

## One Citation

Synchronization in the Kuramoto model in presence of stochastic resetting

- Physics
- 2022

What happens when a system of interacting oscillators of distributed natural frequencies and showing spontaneous collective synchronization in the stationary state is subject to random and repeated…

## References

SHOWING 1-10 OF 75 REFERENCES

Nonstationary coherence-incoherence patterns in nonlocally coupled heterogeneous phase oscillators.

- PhysicsChaos
- 2020

A large ring of nonlocally coupled phase oscillators is considered and it is shown that apart from stationary chimera states, this system also supports nonstationary coherence-incoherence patterns (CIPs), formally describing the infinite system limit.

Emergence of second coherent regions for breathing chimera states.

- PhysicsPhysical review. E
- 2020

Two types of breathing chimeras are demonstrated: the type I breathing chimera looks the same as the stationary chimera at a glance, while the type II consists of multiple coherent regions with different average frequencies.

Spiral wave chimera states in large populations of coupled chemical oscillators

- Physics
- 2017

The coexistence of coherent and incoherent dynamics in a population of identically coupled oscillators is known as a chimera state1,2. Discovered in 20023, this counterintuitive dynamical behaviour…

Chimera states in mechanical oscillator networks

- PhysicsProceedings of the National Academy of Sciences
- 2013

A simple experiment with mechanical oscillators coupled in a hierarchical network is devised to show that chimeras emerge naturally from a competition between two antagonistic synchronization patterns, and a mathematical model shows that the self-organization observed is controlled by elementary dynamical equations from mechanics that are ubiquitous in many natural and technological systems.

Breathing multichimera states in nonlocally coupled phase oscillators.

- Physics, MathematicsPhysical review. E
- 2018

It is numerically demonstrate that breathing multichimera states, whose global order parameter oscillates temporally, can appear and it is shown that the system exhibits a Hopf bifurcation from a stationary multICHimera to a breathing one by the linear stability analysis for the stationary multichIMera.

Imperfect chimera states for coupled pendula

- PhysicsScientific reports
- 2014

It is shown that imperfect chimera can be realized in simple experiments with mechanical oscillators, namely Huygens clock, and that the observed chimera states are controlled by elementary dynamical equations derived from Newton's laws.

Chimera states in a Duffing oscillators chain coupled to nearest neighbors.

- PhysicsChaos
- 2018

This work reports the coexistence of coherent and incoherent domains, called chimera states, in an array of identical Duffing oscillators coupled to their nearest neighbors, characterized by their Lyapunov spectra and their global phase coherence order parameter.

Spectral properties of chimera states.

- PhysicsChaos
- 2011

It is shown that, in this setting, the chimera state is neutrally stable and that the continuous spectrum coincides with the limit of the hyperchaotic Lyapunov spectrum obtained for the finite size systems.

Synchronization patterns and chimera states in complex networks: Interplay of topology and dynamics

- Physics
- 2016

Abstract
We review chimera patterns, which consist of coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics in networks of identical oscillators. We focus on…

Exact results for the Kuramoto model with a bimodal frequency distribution.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

This work derives the system's stability diagram for the special case where the bimodal distribution consists of two equally weighted Lorentzians and shows that in this case the infinite-dimensional problem reduces exactly to a flow in four dimensions.