Phase synchronization and topological defects in inhomogeneous media

Davidsen, Jörn; Kapral, Raymond

doi:10.1103/physreve.66.055202

Cited by 13 publications

(11 citation statements)

References 26 publications

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“…For the phase concept to be utilized, the frequencies of the signal should be locked, otherwise multiple harmonics of these frequencies may overlap and lead to ambiguous phase information [Chen and Nitz, 2003]. Further, the concept of phase synchronization can be applied only to a homogeneous medium [Davidson and Kapral, 2002], which is an unrealistic assumption for the brain. The situation is complicated also by a nonstationary process in the nonlinear phase (de)synchronization measure [Breakspear, 2002].…”

Section: Appendix B Methodological Aspects Of the Index Of Eeg Structmentioning

confidence: 99%

Enhancement of GABA‐related signalling is associated with increase of functional connectivity in human cortex

Fingelkurts¹,

Fingelkurts²,

Kivisaari³

et al. 2004

Human Brain Mapping

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Structural or operational synchrony analysis with EEG was conducted in order to detect functional interaction between cortical areas during an enhanced inhibition induced by the GABAergic agonist lorazepam in a double-blind, randomized, placebo-controlled, cross-over study in eight healthy human subjects. Specifically, we investigated whether a neuronal inhibitory system in the brain mediates functional decoupling of cortical areas. Single-dose lorazepam administration resulted in a widespread increase in the inter-area functional connectivity and an increase in the strength of functional long-range and interhemispheric connections. These results suggest that inhibition can be an efficient mechanism for synchronization of large neuronal populations.

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Section: Appendix B Methodological Aspects Of the Index Of Eeg Structmentioning

confidence: 99%

Enhancement of GABA‐related signalling is associated with increase of functional connectivity in human cortex

Fingelkurts¹,

Fingelkurts²,

Kivisaari³

et al. 2004

Human Brain Mapping

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show abstract

“…This is because the connectivity prevents one from isolating a single sine term like in Eq. (21). However, the linear approach is still applicable in 2D, since the linear solution, Eq.…”

Section: Phase-locked Solutionmentioning

confidence: 99%

Vortices and the entrainment transition in the two-dimensional Kuramoto model

et al. 2010

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We study synchronization in the two-dimensional lattice of coupled phase oscillators with random intrinsic frequencies. When the coupling K is larger than a threshold K E , there is a macroscopic cluster of frequencysynchronized oscillators. We explain why the macroscopic cluster disappears at K E . We view the system in terms of vortices, since cluster boundaries are delineated by the motion of these topological defects. In the entrained phase ͑K Ͼ K E ͒, vortices move in fixed paths around clusters, while in the unentrained phase ͑K Ͻ K E ͒, vortices sometimes wander off. These deviant vortices are responsible for the disappearance of the macroscopic cluster. The regularity of vortex motion is determined by whether clusters behave as single effective oscillators. The unentrained phase is also characterized by time-dependent cluster structure and the presence of chaos. Thus, the entrainment transition is actually an order-chaos transition. We present an analytical argument for the scaling K E ϳ K L for small lattices, where K L is the threshold for phase locking. By also deriving the scaling K L ϳ log N, we thus show that K E ϳ log N for small N, in agreement with numerics. In addition, we show how to use the linearized model to predict where vortices are generated.

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“…This provides an explanation of recent experimental observations and numerical simulations of noise-induced phase synchronization [7,8] (see also [9,29]). Our work also motivates further studies of the internal structure and geometry of synchronization defects in spiral waves in oscillatory media which have been areas of keen interest in recent times [30,31].…”

Section: Discussionmentioning

confidence: 57%

Geometric framework for phase synchronization in coupled noisy nonlinear systems

Balakrishnan

2006

Phys. Rev. E

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A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behavior through a change of stability via a Hopf bifurcation entails the spontaneous appearance of a gauge structure in the system, arising from the evolution of the slow dynamics, but induced by the fast variables. The conditions for the oscillators to be synchronised in phase are obtained. The role of weak noise appears to be to drive the system towards a more synchronized behavior. Our analysis provides a framework to explain recent experimental observations on noise-induced phase synchronization in coupled nonlinear systems.

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Phase synchronization and topological defects in inhomogeneous media

Cited by 13 publications

References 26 publications

Enhancement of GABA‐related signalling is associated with increase of functional connectivity in human cortex

Enhancement of GABA‐related signalling is associated with increase of functional connectivity in human cortex

Vortices and the entrainment transition in the two-dimensional Kuramoto model

Geometric framework for phase synchronization in coupled noisy nonlinear systems

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