Synchronization of coupled oscillators on small-world networks

Mori, Fumito; Odagaki, Takashi

doi:10.1016/j.physd.2009.04.002

Cited by 9 publications

(5 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…5 ): with the same structural connectivity strength, the real connectome was more efficient to synchronize the oscillators than the shuffled versions. This is consistent with past results pointing out the structural efficiency of small-world network to synchronize large number of oscillators [57] – [60] . However, the transition between the two dynamical states (desynchronized and synchronized) was also larger in the real anatomical case (see related C intra intervals in Fig.…”

Section: Discussionsupporting

confidence: 93%

Anatomical Connectivity Influences both Intra- and Inter-Brain Synchronizations

et al. 2012

View full text Add to dashboard Cite

Recent development in diffusion spectrum brain imaging combined to functional simulation has the potential to further our understanding of how structure and dynamics are intertwined in the human brain. At the intra-individual scale, neurocomputational models have already started to uncover how the human connectome constrains the coordination of brain activity across distributed brain regions. In parallel, at the inter-individual scale, nascent social neuroscience provides a new dynamical vista of the coupling between two embodied cognitive agents. Using EEG hyperscanning to record simultaneously the brain activities of subjects during their ongoing interaction, we have previously demonstrated that behavioral synchrony correlates with the emergence of inter-brain synchronization. However, the functional meaning of such synchronization remains to be specified. Here, we use a biophysical model to quantify to what extent inter-brain synchronizations are related to the anatomical and functional similarity of the two brains in interaction. Pairs of interacting brains were numerically simulated and compared to real data. Results show a potential dynamical property of the human connectome to facilitate inter-individual synchronizations and thus may partly account for our propensity to generate dynamical couplings with others.

show abstract

Section: Discussionsupporting

confidence: 93%

Anatomical Connectivity Influences both Intra- and Inter-Brain Synchronizations

et al. 2012

View full text Add to dashboard Cite

show abstract

“…On the other hand, conditions such as these are rarely addressed when studying Kuramoto oscillators in networks. Seeking to fill this gap, Mori and Odagaki [88,89] carried out an interesting analysis through which necessary conditions for frequency synchronization were derived. The analysis in [88] is based on the concept of surface area of sets of nodes in a network.…”

Section: Further Approachesmentioning

confidence: 99%

The Kuramoto model in complex networks

et al. 2016

View full text Add to dashboard Cite

Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

show abstract

“…Small-world topology combines local and long-range connections, thereby decreasing the average path length between cells [17] . Such organization was shown to lead to more efficient synchronization at a lower energy cost (because fewer connections are needed) [18] , [19] , [20] , [21] , [22] . It is thus reasonable to assume that the SCN also exploits such network properties to efficiently synchronize neurons.…”

Section: Introductionmentioning

confidence: 99%

Effect of Network Architecture on Synchronization and Entrainment Properties of the Circadian Oscillations in the Suprachiasmatic Nucleus

2012

View full text Add to dashboard Cite

In mammals, the suprachiasmatic nucleus (SCN) of the hypothalamus constitutes the central circadian pacemaker. The SCN receives light signals from the retina and controls peripheral circadian clocks (located in the cortex, the pineal gland, the liver, the kidney, the heart, etc.). This hierarchical organization of the circadian system ensures the proper timing of physiological processes. In each SCN neuron, interconnected transcriptional and translational feedback loops enable the circadian expression of the clock genes. Although all the neurons have the same genotype, the oscillations of individual cells are highly heterogeneous in dispersed cell culture: many cells present damped oscillations and the period of the oscillations varies from cell to cell. In addition, the neurotransmitters that ensure the intercellular coupling, and thereby the synchronization of the cellular rhythms, differ between the two main regions of the SCN. In this work, a mathematical model that accounts for this heterogeneous organization of the SCN is presented and used to study the implication of the SCN network topology on synchronization and entrainment properties. The results show that oscillations with larger amplitude can be obtained with scale-free networks, in contrast to random and local connections. Networks with the small-world property such as the scale-free networks used in this work can adapt faster to a delay or advance in the light/dark cycle (jet lag). Interestingly a certain level of cellular heterogeneity is not detrimental to synchronization performances, but on the contrary helps resynchronization after jet lag. When coupling two networks with different topologies that mimic the two regions of the SCN, efficient filtering of pulse-like perturbations in the entrainment pattern is observed. These results suggest that the complex and heterogeneous architecture of the SCN decreases the sensitivity of the network to short entrainment perturbations while, at the same time, improving its adaptation abilities to long term changes.

show abstract

Synchronization of coupled oscillators on small-world networks

Cited by 9 publications

References 20 publications

Anatomical Connectivity Influences both Intra- and Inter-Brain Synchronizations

Anatomical Connectivity Influences both Intra- and Inter-Brain Synchronizations

The Kuramoto model in complex networks

Effect of Network Architecture on Synchronization and Entrainment Properties of the Circadian Oscillations in the Suprachiasmatic Nucleus

Contact Info

Product

Resources

About