Synchronization in lattice-embedded scale-free networks

Tauro, Carolina B.; Tamarit, Francisco A.; Gleiser, Pablo M.

doi:10.1016/j.physa.2011.08.012

Cited by 4 publications

(4 citation statements)

References 16 publications

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“…Tauro et al [27] recently analyzed the effects of embedding a scale-free network in the synchronization of phase oscillators. They observed that this network structure allows for the emergence of multiple clusters synchronized at different frequencies.…”

Section: Resultsmentioning

confidence: 99%

“…3(a) and 3(b). On the other hand, shifting the embedding parameters towards smaller values or increasing the scale-free exponent α limits the number of connections available to hubs, and clustered structures emerge [27].…”

Section: Resultsmentioning

confidence: 99%

“…Also, by incorporating both a scale-free network and an embedding in the complex network structure the neurons which are close have many connections, and the connections become sparse with distance [12]. This effect can be tuned with the parameters of the model to obtain extreme cases, such as a regular lattice, or a mean field interaction [27]. In this way we can compare the results of the model with known systems.…”

Section: The Modelmentioning

confidence: 99%

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Modeling spatial patterns in the visual cortex

et al. 2014

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We propose a model for the formation of patterns in the visual cortex. The dynamical units of the model are Kuramoto phase oscillators that interact through a complex network structure embedded in two dimensions. In this way the strength of the interactions takes into account the geographical distance between units. We show that for different parameters, clustered or striped patterns emerge. Using the structure factor as an order parameter we are able to quantitatively characterize these patterns and present a phase diagram. Finally, we show that the model is able to reproduce patterns with cardinal preference, as observed in ferrets.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: The Modelmentioning

confidence: 99%

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Modeling spatial patterns in the visual cortex

et al. 2014

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“…This allows for the introduction of an interaction function that varies with distance. Recently, we proposed a simple model that includes this characteristic, and allows for the emergence of patterns like the ones observed in the visual cortex [2,3]. In particular, we analyzed the behavior of a Kuramoto model of coupled phase oscillators [27][28][29] with competing interactions in a complex network embedded in two-dimensional Euclidean space [3].…”

Section: Modelmentioning

confidence: 99%

Interplay of network structure and dynamics in functional organization of the visual cortex

Gleiser

Tamarit

2018

Phys. Rev. E

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The functional patterns of the visual cortex observed in some mammals such as cats, primates, and humans has allowed us to understand basic principles of organization in the structure of the cortex. However, the observation of different kinds of functional arrangement in other animals such as mice, rats, rabbits, and squirrels, called salt and pepper patterns, raise questions about which of these principles can be transferred to the understanding of visual processing in general. In order to gain insight into these basic principles, in this work we propose a simple model for the formation of spatiotemporal patterns in the visual cortex. The model is based on coupled phase oscillators that interact through an evolving complex network that is embedded in a two-dimensional Euclidean space. In this way we are able to explore the relation between network structure and functional organization. We find that the model allows for the emergence of clustered synchronized states that are spatially segregated as some orientation maps, and also synchronized states that are spatially interspersed, resembling salt and pepper organizational maps.

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Observer-based synchronization in fractional-order leader–follower complex networks

Wang

Zeng

2013

Nonlinear Dyn

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Synchronization in lattice-embedded scale-free networks

Cited by 4 publications

References 16 publications

Modeling spatial patterns in the visual cortex

Modeling spatial patterns in the visual cortex

Interplay of network structure and dynamics in functional organization of the visual cortex

Observer-based synchronization in fractional-order leader–follower complex networks

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