# Stability of amplitude chimeras in oscillator networks

@article{Tumash2016StabilityOA, title={Stability of amplitude chimeras in oscillator networks}, author={Liudmila Tumash and A. S. Zakharova and Judith Lehnert and Wolfram Just and Eckehard Sch{\"o}ll}, journal={Europhysics Letters}, year={2016}, volume={117} }

We show that amplitude chimeras in ring networks of Stuart-Landau oscillators with symmetry-breaking nonlocal coupling represent saddle-states in the underlying phase space of the network. Chimera states are composed of coexisting spatial domains of coherent and of incoherent oscillations. We calculate the Floquet exponents and the corresponding eigenvectors in dependence upon the coupling strength and range, and discuss the implications for the phase-space structure. The existence of at least…

## 16 Citations

### Networks of coupled oscillators: From phase to amplitude chimeras.

- PhysicsChaos
- 2018

It is found numerically that the amplitude chimeras are not short-living transients but can have a long lifetime and qualitative explanation of the observed phenomena in the light of symmetry breaking bifurcation scenarios is provided.

### Stable amplitude chimera states in a network of locally coupled Stuart-Landau oscillators.

- PhysicsChaos
- 2018

It is found that while a small perturbation allows one to perturb a large number of oscillators resulting in a stable amplitude chimera state, a large perturbations allows a small number ofscillators to be perturbated to get a stable amplifying state.

### Freak chimera states in a locally coupled Duffing oscillators chain

- PhysicsCommun. Nonlinear Sci. Numer. Simul.
- 2020

### 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.

### Imperfect Amplitude Mediated Chimera States in a Nonlocally Coupled Network

- PhysicsFront. Appl. Math. Stat.
- 2018

The employed attractive and repulsive couplings induce imperfect amplitude mediated chimera state which emerges as an intermediate between the oscillatory dynamics and the oscillation death state, which exponentially decays as a function of the coupling range and obeys a power law relation.

### Small amplitude chimeras for coupled clocks

- PhysicsNonlinear Dynamics
- 2020

We report the arise of small amplitude chimera states in three coupled pendulum clocks suspended on an oscillating base. Two types of chimeras are identified and described by the character of the…

### Amplitude chimera and chimera death induced by external agents in two-layer networks.

- PhysicsChaos
- 2020

Stable amplitude chimeras and chimera death in a two-layer network where one layer has an ensemble of identical nonlinear oscillators interacting directly through local coupling and indirectly through dynamic agents that form the second layer are reported.

### Filtering Suppresses Amplitude Chimeras

- PhysicsFront. Appl. Math. Stat.
- 2019

It is quantitatively established that with decreasing cut-off frequency of the filter, an AC transforms into a synchronized pattern and shows that the symmetry-breaking steady state can be revoked and rhythmogenesis can be induced by local filtering.

### Distinct collective states due to trade-off between attractive and repulsive couplings.

- PhysicsPhysical review. E
- 2018

The emergence of various cluster chimera death states through a dynamically distinct transition route, namely the oscillatory cluster state and coherent oscillation death state as a function of the repulsive coupling in the presence of the attractive coupling is shown.

## References

SHOWING 1-10 OF 35 REFERENCES

### Transient scaling and resurgence of chimera states in networks of Boolean phase oscillators.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

The average transient time of nonlocally coupled electronic oscillators is found to increase exponentially with the network size and can be modeled as a Poisson process in experiment and simulation.

### Stable and transient multicluster oscillation death in nonlocally coupled networks.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

Going beyond standard mean-field theory, the boundaries of the different stability regimes as well as the transient times analytically are predicted in excellent agreement with numerical results.

### Chimera-like States in Modular Neural Networks

- BiologyScientific reports
- 2016

Analysis of a neural network inspired by the connectome of the C. elegans soil worm, organized into six interconnected communities, suggests that under certain assumptions, chimera-like states are prominent phenomena in modular networks, and might provide insight for the behavior of more complex modular networks.

### Control of self-organizing nonlinear systems

- Mathematics
- 2016

Controlling chimera patterns in networks: Interplay of structure, noise, and delay.- Emergence of clusters of locked and whirling oscillators in the Kuramoto model with Inertia.- Control of…

### Phys

- Rev. E 93, 012209
- 2016

### Phys

- Rev. Lett. 112, 154101
- 2014

### Phys

- Rev. Lett. 112, 144101
- 2014

### Phys

- Rev. E 94, 032206
- 2016

### Phys

- Rev. E 92, 042919 Fig. 8: (a) Space-time plot of an amplitude chimera state yj(t) in a very small network. (b) Phase portrait. Parameters: N = 12, λ = 1, ω = 2, r = 1 12 , σ = 5.
- 2015