Phase resetting and transient desynchronization in networks of globally coupled phase oscillators with inertia

Dolan, Kevin; Majtanik, Milan; Tass, Peter A.

doi:10.1016/j.physd.2005.08.009

Cited by 17 publications

(12 citation statements)

References 30 publications

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“…However, they do cite papers related to Parkinson's disease where the Kuramoto model is specifically mentioned. Interestingly, in brain activity studies, the Kuramoto model is playing a quite important role in the study of desynchronisation in the context of pulse based desynchronisation techniques for the treatment of Parkinson's disease [103,122,123]. However, such investigations give no insight about the nature of the initiation of the synchronisation in either epilepsy or Parkinson's disease.…”

Section: F3 the Kuramoto Model And Epilepsymentioning

confidence: 99%

Understanding the abnormal brain activity in epilepsy as a potential predictor of the onset of an epileptic seizure

Dunn¹,

Abbott²,

Masterton³

et al. 2011

ANZIAMJ

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The Brain Research Institute (bri) uses various types of indirect measurements, including eeg and fmri, to understand and assess brain activity and function. As well as the recovery of generic information about brain function, research also focuses on the utilisation of such data and understanding to study the initiation, dynamics, spread and suppression of epileptic seizures. To assist with the future focussing of this aspect of their research, the bri asked the misg 2010 participants to examine how the available eeg and fmri data and current knowledge about epilepsy should be analysed and interpreted to yield an enhanced understanding about brain activity occurring before, at commencement of, during, and after a seizure. Though the deliberations of the study group were wide ranging in terms of the related matters considered and discussed, considerable progress was

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Section: F3 the Kuramoto Model And Epilepsymentioning

confidence: 99%

Understanding the abnormal brain activity in epilepsy as a potential predictor of the onset of an epileptic seizure

Dunn¹,

Abbott²,

Masterton³

et al. 2011

ANZIAMJ

View full text Add to dashboard Cite

show abstract

“…A detailed description of this model has been presented by Dolan et al [38]. The model is an extension of a well-elaborated second order phaseoscillator model originally proposed by Haken as an approximation for the dynamics of a neuron consisting of an axon and dendrite [39].…”

Section: The Modelmentioning

confidence: 99%

“…At the stimulation amplitude I stim = H ≈ 4.1ω, the oscillatory regime disappears, and all initial stimulation phases result in the quiet regime. This corresponds to the case of stimulation of individual oscillators where the homoclinic bifurcation occurs, and all initial conditions go to the stable fixed point [38].…”

Section: Dynamics Of the Network Under Continuous Stimulationmentioning

confidence: 99%

“…This is because a fully desynchronized network will resynchronize faster when there is a range of phase velocities at the time of full desynchronization, than when the neurons all have approximately the same phase velocity [38].…”

Section: Velocity Distribution Effects On Resynchronization Timementioning

confidence: 99%

“…This is because the uniformly distributed phases, combined with a δ-like velocity distribution at the eigenfrequency of the oscillators, constitutes a fixed point in the phase space of the network [38]. This fixed point is unstable, but when the system is at that fixed point, the effect of the coupling vanishes.…”

Section: Velocity Distribution Effects On Resynchronization Timementioning

confidence: 99%

See 2 more Smart Citations

Desynchronization in Networks of Globally Coupled Neurons with Dendritic Dynamics

Majtanik¹,

Dolan²,

Tass

2006

J Biol Phys

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Effective desynchronization can be exploited as a tool for probing the functional significance of synchronized neural activity underlying perceptual and cognitive processes or as a mild treatment for neurological disorders like Parkinson's disease. In this article we show that pulse-based desynchronization techniques, originally developed for networks of globally coupled oscillators (Kuramoto model), can be adapted to networks of coupled neurons with dendritic dynamics. Compared to the Kuramoto model, the dendritic dynamics significantly alters the response of the neuron to the stimulation. Under medium stimulation amplitude a bistability of the response of a single neuron is observed. When stimulated at some initial phases, the neuron displays only modulations of its firing, whereas at other initial phases it stops oscillating entirely. Significant alterations in the duration of stimulation-induced transients are also observed. These transients endure after the end of the stimulation and cause maximal desynchronization to occur not during the stimulation, but with some delay after the stimulation has been turned off. To account for this delayed desynchronization effect, we have designed a new calibration procedure for finding the stimulation parameters that result in optimal desynchronization. We have also developed a new desynchronization technique by low frequency entrainment. The stimulation techniques originally developed for the Kuramoto model, when using the new calibration procedure, can also be applied to networks with dendritic dynamics. However, the mechanism by which desynchronization is achieved is substantially different than for the network of Kuramoto oscillators. In particular, the addition of dendritic dynamics significantly changes the timing of the stimulation required to obtain desynchronization. We propose desynchronization stimulation for experimental analysis of synchronized neural processes and for the therapy of movement disorders.

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Brain Pacemaker

Tass

Popovych²,

Hauptmann³

2009

Encyclopedia of Complexity and Systems Science

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Phase resetting and transient desynchronization in networks of globally coupled phase oscillators with inertia

Cited by 17 publications

References 30 publications

Understanding the abnormal brain activity in epilepsy as a potential predictor of the onset of an epileptic seizure

Understanding the abnormal brain activity in epilepsy as a potential predictor of the onset of an epileptic seizure

Desynchronization in Networks of Globally Coupled Neurons with Dendritic Dynamics

Brain Pacemaker

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