Symmetry- and input-cluster synchronization in networks

Siddique, Abu Bakar; Pecora, Louis M.; Hart, Joseph D.; Sorrentino, Francesco

doi:10.1103/physreve.97.042217

Cited by 80 publications

(76 citation statements)

References 9 publications

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“…11c. These experiments confirm the stability of such so-called equitable partition cluster synchronization [34].…”

Section: Experimental Examplessupporting

confidence: 77%

“…There are two major benefits to this network implementation: this is the only way to create a network of truly identical nodes, and it allows one to implement a large network without building a large number of separate physical nodes. While originally used for a hardware implementation of reservoir computing [29,30,35,58,59,60], these types of delay systems have since been used to study chimera states in cyclic networks [31,32] and cluster synchronization in arbitrary networks [33,34]. Because delay systems require a continuous function to describe their initial conditions, they are considered infinite dimensional systems.…”

Section: Space-time Representationmentioning

confidence: 99%

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Delayed dynamical systems: networks, chimeras and reservoir computing

Hart

Larger

Murphy

et al. 2019

Phil. Trans. R. Soc. A.

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We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics, extensive research on optoelectronic feedback loops has revealed their immense potential for realizing complex system dynamics such as chimeras in rings of coupled oscillators and applications to reservoir computing. Delayed dynamical systems have been enriched in recent years through the application of digital signal processing techniques. Very recently, we have showed that one can significantly extend the capabilities and implement networks with arbitrary topologies through the use of field programmable gate arrays (FPGAs). This architecture allows the design of appropriate filters and multiple time delays which greatly extend the possibilities for exploring synchronization patterns in arbitrary topological networks. This has enabled us to explore complex dynamics on networks with nodes that can be perfectly identical, introduce parameter heterogeneities and multiple time delays, as well as change network topologies to control the formation and evolution of patterns of synchrony.

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“…11c. These experiments confirm the stability of such so-called equitable partition cluster synchronization [34].…”

Section: Experimental Examplessupporting

confidence: 77%

Section: Space-time Representationmentioning

confidence: 99%

Delayed dynamical systems: networks, chimeras and reservoir computing

Hart

Larger

Murphy

et al. 2019

Phil. Trans. R. Soc. A.

Self Cite

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“…These papers studied complete synchronization (all nodes synchronize on the same time-evolution) and consider diffusive coupling (the coupling matrices are Laplacian). Populations may exhibit more complex forms of synchronization, such as clustered synchronization (CS), where clusters of nodes exhibit synchronized dynamics but different clusters evolve on distinct time evolutions; many papers consider CS in networks formed of nodes all of the same type and connections all of the same type [17][18][19][20][21][22][23][24] .…”

mentioning

confidence: 99%

Symmetries and cluster synchronization in multilayer networks

et al. 2020

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Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the emergence of cluster synchronization in these networks. We distinguish between independent layer symmetries, which occur in one layer and are independent of the other layers, and dependent layer symmetries, which involve nodes in different layers. We study stability of the cluster synchronous solution by decoupling the problem into a number of independent blocks and assessing stability of each block through a Master Stability Function. We see that blocks associated with dependent layer symmetries have a different structure to the other blocks, which affects the stability of clusters associated with these symmetries. Finally, we validate the theory in a fully analog experiment in which seven electronic oscillators of three kinds are connected with two kinds of coupling.

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“…On the whole, the method (based on the multi-layer network formalism) can be used to analyze exact cluster synchronization (CS) in neuron networks with directed connections, delays, couplings that depend on both the presynaptic and the postsynaptic neurons, and different kinds of nodes and synapses. The main novelty is the generalization to this general framework of a stability analysis method previously developed for a tighter class of networks [12][13][14][15][16][17][18][19][20] . Our goal is to achieve improved understanding of the causal influence that each network element exerts on the other elements, thus shedding light on how functions emerge from structural connectivity, combined with neuronal dynamics.…”

mentioning

confidence: 99%

Analyzing synchronized clusters in neuron networks

Lodi

Rossa

Sorrentino

et al. 2020

Sci Rep

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The presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing. Common approaches to study cluster synchronization in networks of coupled oscillators ground on simplifying assumptions, which often neglect key biological features of neuron networks. Here we propose a general framework to study presence and stability of synchronous clusters in more realistic models of neuron networks, characterized by the presence of delays, different kinds of neurons and synapses. Application of this framework to two examples with different size and features (the directed network of the macaque cerebral cortex and the swim central pattern generator of a mollusc) provides an interpretation key to explain known functional mechanisms emerging from the combination of anatomy and neuron dynamics. The cluster synchronization analysis is carried out also by changing parameters and studying bifurcations. Despite some modeling simplifications in one of the examples, the obtained results are in good agreement with previously reported biological data.

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Symmetry- and input-cluster synchronization in networks

Cited by 80 publications

References 9 publications

Delayed dynamical systems: networks, chimeras and reservoir computing

Delayed dynamical systems: networks, chimeras and reservoir computing

Symmetries and cluster synchronization in multilayer networks

Analyzing synchronized clusters in neuron networks

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