Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplexes.

@article{Skardal2019AbruptDA,
  title={Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplexes.},
  author={Per Sebastian Skardal and Alex Arenas},
  journal={Physical review letters},
  year={2019},
  volume={122 24},
  pages={
          248301
        }
}
Collective behavior in large ensembles of dynamical units with nonpairwise interactions may play an important role in several systems ranging from brain function to social networks. Despite recent work pointing to simplicial structure, i.e., higher-order interactions between three or more units at a time, their dynamical characteristics remain poorly understood. Here we present an analysis of the collective dynamics of such a simplicial system, namely coupled phase oscillators with three-way… 

Figures from this paper

Spectrum of extensive multiclusters in the Kuramoto model with simplicial interaction.

TLDR
This work provides a rigorous description of the stability of various multicluster states by studying their spectral properties in the thermodynamic limit and shows that, similar to the classical Kuramoto model, the drifting subpopulation of any state has a continuous spectra confined to the imaginary axis and the negative real axis.

Exact solutions of the abrupt synchronization transitions and extensive multistability in globally coupled phase oscillator populations

The Kuramoto model consisting of large ensembles of globally coupled phase oscillators serves as a paradigm for modelling synchronization and collective behavior in diverse self-sustained systems. As

Higher order interactions in complex networks of phase oscillators promote abrupt synchronization switching

TLDR
These findings reveal a self-organized phenomenon that may be responsible for the rapid switching to synchronization in many biological and other systems that exhibit synchronization without the need of particular correlation mechanisms between the oscillators and the topological structure.

Stability of synchronization in simplicial complexes

TLDR
This work shows that complete synchronization exists as an invariant solution, and gives the necessary condition for it to be observed as a stable state, and generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture.

Bifurcation and structural stability of simplicial oscillator populations: Exact results

We present an analytical description for the collective dynamics of oscillator ensembles with higher-order coupling encoded by simplicial structure, which serves as an illustrative and insightful

Bifurcation analysis and structural stability of simplicial oscillator populations

We present an analytical description for the collective dynamics of oscillator ensembles with higher-order coupling encoded by simplicial structure, which serves as an illustrative and insightful

Multistability in coupled oscillator systems with higher-order interactions and community structure

We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to

Multiorder Laplacian for synchronization in higher-order networks

TLDR
A multi-order Laplacian framework is introduced that allows for a complete analytical characterization of the stability of synchrony in arbitrary higher-order networks, paving the way towards a general treatment of dynamical processes beyond pairwise interactions.

Hysteresis and synchronization processes of Kuramoto oscillators on high-dimensional simplicial complexes with competing simplex-encoded couplings.

TLDR
These findings shed new light on the mechanisms by which the high-dimensional simplicial complexes in natural systems, such as human connectomes, can modulate their native synchronization processes.

Discordant synchronization patterns on directed networks of identical phase oscillators with attractive and repulsive couplings.

TLDR
By employing the dimensional reduction scheme of the Ott-Antonsen (OA) theory, the existence of traveling wave and π-states is verified, in addition to the classical fully synchronized and incoherent states.
...

References

SHOWING 1-10 OF 40 REFERENCES

Chaos in generically coupled phase oscillator networks with nonpairwise interactions.

TLDR
It is shown that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values and can give rise to complex emergent dynamics in symmetric phase oscillator networks.

Multistable attractors in a network of phase oscillators with three-body interactions.

TLDR
Owing to the infinite multistability, the degree of synchrony in an asymptotic state can vary continuously within some range depending on the initial phase pattern.

Cluster synchrony in systems of coupled phase oscillators with higher-order coupling.

TLDR
For the first time, a complete analytic description of the dynamics in the limit of a large number of oscillators is developed and used to quantify the degree of cluster synchrony, cluster asymmetry, and switching.

Complex Network Geometry and Frustrated Synchronization

TLDR
This work reveals the rich interplay between network geometry and synchronization of coupled oscillators in the context of a simplicial complex model of manifolds called Complex Network Manifold and shows that the networks display frustrated synchronization for a wide range of the coupling strength of the oscillators.

Dynamics on Networks of Cluster States for Globally Coupled Phase Oscillators

TLDR
This paper shows that navigation may be done reliably even in the presence of noise and frequency detuning, as long as the input amplitude dominates the noise strength and the detuning magnitude, and the time between the applied pulses is in a suitable range.

Disorder induces explosive synchronization.

TLDR
It is shown that explosive synchronization can be induced in mildly heterogeneous networks by the addition of quenched disorder to the oscillators' frequencies, demonstrating that it is not only robust to, but moreover promoted by, this natural mechanism.

Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks

TLDR
Light is shed on the intimate connection between network symmetry and cluster synchronization and general tech-niques are introduced that use network symmetries to reveal the patterns of synchronized clusters and determinethe conditions under which they persist.

Control of coupled oscillator networks with application to microgrid technologies

TLDR
This work develops a method for control based on identifying and stabilizing problematic oscillators, resulting in a stable spectrum of eigenvalues, and in turn a linearly stable synchronized state.

Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling.

TLDR
Finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field is reported on, which microscopically is equivalent to a hypernetwork organization of interactions and argues that a transition to synchronies occurs only for finite-size ensembles and disappears in the thermodynamic limit.

Long time evolution of phase oscillator systems.

It is shown, under weak conditions, that the dynamical evolution of large systems of globally coupled phase oscillators with Lorentzian distributed oscillation frequencies is, in an appropriate