Multiclusters in Networks of Adaptively Coupled Phase Oscillators

@article{Berner2019MulticlustersIN,
  title={Multiclusters in Networks of Adaptively Coupled Phase Oscillators},
  author={Rico Berner and Eckehard Sch{\"o}ll and Serhiy Yanchuk},
  journal={SIAM J. Appl. Dyn. Syst.},
  year={2019},
  volume={18},
  pages={2227-2266}
}
Dynamical systems on networks with adaptive couplings appear naturally in real-world systems such as power grid networks, social networks as well as neuronal networks. We investigate a paradigmatic system of adaptively coupled phase oscillators inspired by neuronal networks with synaptic plasticity. One important behaviour of such systems reveals splitting of the network into clusters of oscillators with the same frequencies, where different clusters correspond to different frequencies… Expand
Effect of diluted connectivities on cluster synchronization of adaptively coupled oscillator networks
TLDR
This work investigates the robustness of multicluster states on networks of adaptively coupled Kuramoto-Sakaguchi oscillators against the random dilution of the underlying network topology, utilizing the master stability approach for adaptive networks in order to highlight the interplay between adaptivity and topology. Expand
Multicluster States in Adaptive Networks of Coupled Phase Oscillators
  • R. Berner
  • Physics
  • Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators
  • 2021
In this chapter, we analyze multicluster states in a network of adaptively coupled phase oscillators. Multicluster states are composed of several one-clusters with distinct frequencies. Starting fromExpand
Interplay of adaptivity and multiplexing in networks of adaptively coupled phase oscillators
TLDR
It is shown by theoretical analysis and computer simulations that multiplexing in a multi-layer network with symmetry can induce various stable phase cluster states in a situation where they are not stable or do not even exist in the single layer. Expand
Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks.
TLDR
It is shown by theoretical analysis and computer simulations that multiplexing in a multilayer network with symmetry can induce various stable phase cluster states in a situation where they are not stable or do not even exist in the single layer. Expand
When three is a crowd: Chaos from clusters of Kuramoto oscillators with inertia.
TLDR
Through rigorous analysis and numerics, it is demonstrated that the intercluster phase shifts can stably coexist and exhibit different forms of chaotic behavior, including oscillatory, rotatory, and mixed-mode oscillations. Expand
Generalized splay states in phase oscillator networks.
TLDR
This article introduces generalized m-splay states constituting a special subclass of phase-locked states with vanishing mth order parameter, and provides explicit linear stability conditions for splay states. Expand
What adaptive neuronal networks teach us about power grids.
TLDR
It is proved that phase oscillator models with inertia can be viewed as a particular class of adaptive networks, and the phenomenon of cascading line failure in power grids is translated into an adaptive neuronal network. Expand
Continuum Limits for Adaptive Network Dynamics
Adaptive (or co-evolutionary) network dynamics, i.e., when changes of the network/graph topology are coupled with changes in the node/vertex dynamics, can give rise to rich and complex dynamicalExpand
Modelling power grids as pseudo adaptive networks
Power grids, as well as neuronal networks with synaptic plasticity, describe real-world systems of tremendous importance for our daily life. The investigation of these seemingly unrelated types ofExpand
Splay states and two-cluster states in ensembles of excitable units
Focusing on systems of sinusoidally coupled active rotators, we study the emergence and stability of periodic collective oscillations for systems of identical excitable units with repulsiveExpand
...
1
2
3
4
...

References

SHOWING 1-10 OF 66 REFERENCES
Self-organized network of phase oscillators coupled by activity-dependent interactions.
  • Takaaki Aoki, T. Aoyagi
  • Mathematics, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2011
We investigate a network of coupled phase oscillators whose interactions evolve dynamically depending on the relative phases between the oscillators. We found that this coevolving dynamical systemExpand
Cluster and group synchronization in delay-coupled networks.
TLDR
This work investigates the stability of synchronized states in delay-coupled networks where synchronization takes place in groups of different local dynamics or in cluster states in networks with identical local dynamics and finds that the master stability function shows a discrete rotational symmetry depending on the number of groups. Expand
Clustering in delay-coupled smooth and relaxational chemical oscillators.
TLDR
Extending the theory on Hopf normal-form oscillators, the theory is able to account for realistic interaction functions, yielding good agreement with experimental findings. Expand
Two-cluster bifurcations in systems of globally pulse-coupled oscillators
Abstract For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all stationary two-cluster states and explain how theExpand
Oscillatory cluster patterns in a homogeneous chemical system with global feedback
TLDR
The observation of so-called ‘localized clusters’—periodic antiphase oscillations in one part of the medium, while the remainder appears uniform—in the Belousov–Zhabotinsky reaction–diffusion system with photochemical global feedback is reported. Expand
Plasticity and learning in a network of coupled phase oscillators.
A generalized Kuramoto model of coupled phase oscillators with a slow varying coupling matrix is studied. The dynamics of the coupling coefficients is driven by the phase difference of pairs ofExpand
Emergent explosive synchronization in adaptive complex networks.
TLDR
It is found that the emergent networks spontaneously develop the structural conditions to sustain explosive synchronization and can enlighten the shaping mechanisms at the heart of the structural and dynamical organization of some relevant biological systems, namely, brain networks, for which the emergence of explosive synchronization has been observed. Expand
Controlling cluster synchronization by adapting the topology.
TLDR
An adaptive control scheme for the control of in-phase and cluster synchronization in delay-coupled networks based on the speed-gradient method that opens up possible applications in a wide range of systems in physics, chemistry, technology, and life science. Expand
Adaptive oscillator networks with conserved overall coupling: sequential firing and near-synchronized states.
TLDR
All-to-all networks of nonidentical oscillators with adaptive coupling with spike-timing-dependent plasticity and extended Kuramoto model find multiple phase-locked states that fall into two classes: near-synchronized states and splay states. Expand
Co-evolution of phases and connection strengths in a network of phase oscillators.
TLDR
This model captures the essential characteristics of a class of co-evolving and adaptive networks and exhibits three kinds of asymptotic behavior: a two-cluster state, a coherent state with a fixed phase relation, and a chaotic state with frustration. Expand
...
1
2
3
4
5
...