• Corpus ID: 235624290

Forget Partitions: Cluster Synchronization in Directed Networks Generate Hierarchies

@inproceedings{Brady2021ForgetPC,
  title={Forget Partitions: Cluster Synchronization in Directed Networks Generate Hierarchies},
  author={Fiona M. Brady and Yuanzhao Zhang and Adilson E. Motter},
  year={2021}
}
We present a scalable approach for simplifying the stability analysis of cluster synchronization patterns on directed networks. When a network has directional couplings, decomposition of the coupling matrix into independent blocks (which in turn decouples the variational equation) is no longer adequate to reveal the full relations among perturbation modes. Instead, it is often necessary to introduce directional dependencies among the blocks and establish hierarchies among perturbation modes… 

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References

SHOWING 1-10 OF 76 REFERENCES
One-way dependent clusters and stability of cluster synchronization in directed networks
TLDR
The main contribution of this paper is a method to transform the cluster stability problem in an irreducible form and decompose the original problem into subproblems of the lowest dimension, which allows to immediately detect inter-dependencies among clusters.
Symmetry-Independent Stability Analysis of Synchronization Patterns
TLDR
A generalization of the MSF formalism is established that can characterize the stability of any cluster synchronization pattern, even when the oscillators and/or their interactions are nonidentical, and leads to an algorithm that is error-tolerant and orders of magnitude faster than existing symmetry-based algorithms.
Synchronization and equitable partitions in weighted networks.
The work presented in this paper has two purposes. One is to expose that the coupled cell network formalism of Golubitsky, Stewart, and collaborators accommodates in a natural way the weighted
Dynamics of Coupled Cell Networks: Synchrony, Heteroclinic Cycles and Inflation
TLDR
Focussing on transitive networks that have only one type of cell (identical cell networks), this work addresses three questions relating the network structure to dynamics, and investigates how the dynamics of coupled cell networks with different structures and numbers of cells can be related.
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.
Stability Conditions for Cluster Synchronization in Networks of Heterogeneous Kuramoto Oscillators
TLDR
Quantitative conditions on the network weights, cluster configuration, and oscillators’ natural frequency that ensure the asymptotic stability of the cluster synchronization manifold are derived, showing that cluster synchronization is stable when the intracluster coupling is sufficiently stronger than the intercluster coupling.
Characterization and Computation of Partial Synchronization Manifolds for Diffusive Delay-Coupled Systems
TLDR
This work presents equivalent existence criteria for partial synchronization manifolds in terms of invariant spaces, the block-structure of a reordered adjacency matrix, and the solvability of a Sylvester equation.
Topological Control of Synchronization Patterns: Trading Symmetry for Stability.
TLDR
It is shown that the synchronizability of almost any symmetry cluster in a network of identical nodes can be enhanced precisely by breaking its structural symmetry, which holds for generic node dynamics and arbitrary network structure.
Nonlinear dynamics of networks: the groupoid formalism
A formal theory of symmetries of networks of coupled dynamical systems, stated in terms of the group of permutations of the nodes that preserve the network topology, has existed for some time.
...
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