Global synchronization of partially forced Kuramoto oscillators on networks

Moreira, Carolina A.; Aguiar, Marcus A. M. de

doi:10.1016/j.physa.2018.09.096

Cited by 33 publications

(17 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here we consider a modified version of the original Kuramoto model where each oscillator interacts only with a subset of the other oscillators, as specified by a network of connections [27]. Moreover, part of the oscillators also interacts with an external periodic force [16,[28][29][30]. The force can be interpreted as an external stimulus and the set of oscillators coupled to it represents the 'interface' of the system, like the photo-receptor cells in the eye [8].…”

Section: Methodsmentioning

confidence: 99%

“…Lack of synchronization, on the other hand, suggests difficulty to respond to the stimulus or to function properly, as reported in unsuccessful overnight memory consolidation in old people [12], deficiency in the auditory-motor connections [13] or brain disorders in autistic individuals [14,15]. In this context, the knowledge of the organization of different types of neurons in the network and their segregation into modules or communities is fundamental to understand how stimuli affect the target module and under what conditions it propagates to other regions leading to global or poor responses.In this work we probe the community structure of the neural electrical junction network of the C. elegans using the partially forced Kuramoto model of synchronization [16]. We aim to understand how the network responds to external localized stimuli and which modules are more affected when a specific group of neurons, that can be a functional group or a physically arranged module, is stimulated.…”

mentioning

confidence: 99%

“…We want to investigate the behavior of the system as a function of parameters such as stimulus intensity and inter-neuron connection strength.In particular we are interested in cases leading to global induced synchronization and highly correlated behavior, where the network responds as a whole, or to uncorrelated states, where neurons do not react to each other. Our simulations are guided by the results of a previous paper [16] where we studied the partially forced Kuramoto model on synthetic networks, using the external force to simulate a localized stimulus.C. elegans is a nematode animal, unsegmented and with bilateral symmetry, exhibiting physiological similarity to mammals as regards the nerves and neurotransmiters morphologies and it is considered a model organism in studies of disorders related to human nervous system, such as epilepsy [17,18] and Parkinson's disease [19,20].…”

mentioning

confidence: 99%

“…In particular we are interested in cases leading to global induced synchronization and highly correlated behavior, where the network responds as a whole, or to uncorrelated states, where neurons do not react to each other. Our simulations are guided by the results of a previous paper [16] where we studied the partially forced Kuramoto model on synthetic networks, using the external force to simulate a localized stimulus.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Modular structure in C. elegans neural network and its response to external localized stimuli

Moreira

Aguiar

2019

Physica A: Statistical Mechanics and its Applications

Self Cite

View full text Add to dashboard Cite

Synchronization plays a key role in information processing in neuronal networks. Response of specific groups of neurons are triggered by external stimuli, such as visual, tactile or olfactory inputs. Neurons, however, can be divided into several categories, such as by physical location, functional role or topological clustering properties. Here we study the response of the electric junction C. elegans network to external stimuli using the partially forced Kuramoto model and applying the force to specific groups of neurons. Stimuli were applied to topological modules, obtained by the ModuLand procedure, to a ganglion, specified by its anatomical localization, and to the functional group composed of all sensory neurons. We found that topological modules do not contain purely anatomical groups or functional classes, corroborating previous results, and that stimulating different classes of neurons lead to very different responses, measured in terms of synchronization and phase velocity correlations. In all cases, however, the modular structure hindered full synchronization, protecting the system from seizures. More importantly, the responses to stimuli applied to topological and functional modules showed pronounced patterns of correlation or anti-correlation with other modules that were not observed when the stimulus was applied to ganglia.Understanding the network of neuronal connections in the brain is key to unravel the way it works and processes information. The complexity of these networks has been emphasized by many authors [1], and characterized with different measures, such as degree distribution, transitivity and betweenness centrality [2]. An important feature of neural networks is their high degree of heterogeneity, in the sense that the number of connections per neuron varies considerably and typically displays some sort of power law distribution. Moreover, neurons tend to form communities, where the density of connections is higher within than among communities. Because connections are constrained by anatomical features, neurons are also organized into physically arranged clusters, such as lobes or ganglia, where neurons with different functional roles coexist [3][4][5].Communities are often related to specialized areas of the brain and their number and structure are an indication of how many different tasks it can perform [6]. The integration of communities, on the other hand, measures how well the outcomes of these different processes can combined to build a global view of the inputs [3]. When triggered by external stimuli, such as visual or olfactory inputs, the information processing occurs by the synchronized firing of neurons responsible to process those specific tasks [7,8]. Synchronization of larger sets of neurons, or even global synchronization, indicates cerebral disorders [9] such as epilepsy [10] and Alzheimer's disease [11], causing a general breakdown in the neuronal network. Lack of synchronization, on the other hand, suggests difficulty to respond to the stimulus or to function properly,...

show abstract

Section: Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Modular structure in C. elegans neural network and its response to external localized stimuli

Moreira

Aguiar

2019

Physica A: Statistical Mechanics and its Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…The dynamical models for these cases consist commonly in a complex network where the cells, which pertinent dynamical states are described by Kuramoto oscillators, are located at the vertices, with the edges corresponding to the interaction among them. Recent applications of partially forced Kuramoto oscillators include the study of the response to external stimuli of the C. elegans neural network 22,23 (see 24 for a review on complex network models for the response of neural networks to external stimuli), self-organization and pattern formation in the growing and developing of vertebrates 25 , auditory signals in amphibians 26 , and several issues on the circadian rhythm [27][28][29] .…”

Section: Introductionmentioning

confidence: 99%

Optimal global synchronization of partially forced Kuramoto oscillators

Clímaco

Saa

2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

We consider the problem of global synchronization in a large random network of Kuramoto oscillators where some of them are subject to an external periodically driven force. We explore a recently proposed dimensional reduction approach and introduce an effective two-dimensional description for the problem. From the dimensionally reduced model, we obtain analytical predictions for some critical parameters necessary for the onset of a globally synchronized state in the system. Moreover, the low dimensional model also allows us to introduce an optimization scheme for the problem. Our main conclusion, which has been corroborated by exhaustive numerical simulations, is that for a given large random network of Kuramoto oscillators, with random natural frequencies ω i , such that a fraction of them is subject to an external periodic force with frequency Ω, the best global synchronization properties correspond to the case where the fraction of the forced oscillators is chosen to be those ones such that |ω i − Ω| is maximal. Our results might shed some light on the structure and evolution of natural systems for which the presence or the absence of global synchronization are desired properties. Some properties of the optimal forced networks and its relation to recent results in the literature are also discussed.We consider here the dynamics of a large number of interacting Kuramoto oscillators. Each oscillator has its own natural frequency ω i , which is assumed to be a random variable, and the interactions among them are associated with the edges of a random network. Despite of being essentially a random system, there are plenty of robust results obtained from this kind of model which have proven to be relevant in many different areas. This is the case, for instance, of synchronization phenomena, see 1 and 2 for comprehensive reviews on the subject. Here, we are concerned with one of the main variations of the network of Kuramoto oscillators, the case where some of the oscillators are subject to an external periodically driven force with frequency Ω. By exploring a recently proposed analytical approach, we introduce an optimization scheme for the onset of the so-called global synchronization in the system, a regime where all oscillators rigidly rotate, forming a compact swarm, in the same pace of the external force, with frequency Ω. We show that the best global synchronization properties correspond to the case where the set of forced oscillators is chosen to be those ones such that the value of |ω i −Ω| is maximal. Our results may help to understand the evolution and structure of natural systems with many interacting agents for which global synchronization plays an important dynamical role.

show abstract