Refine
Has Fulltext
- no (4)
Year of publication
- 2015 (4) (remove)
Document Type
- Article (4)
Language
- English (4)
Is part of the Bibliography
- yes (4)
Institute
The rhythmic activity observed in nervous systems, in particular in epilepsies and Parkinson's disease, has often been hypothesized to originate from a macroscopic self-sustained neural oscillator. However, this assumption has not been tested experimentally. Here we support this viewpoint with in vivo experiments in a rodent model of absence seizures, by demonstrating frequency locking to external periodic stimuli and finding the characteristic Arnold tongue. This result has important consequences for developing methods for the control of brain activity, such as seizure cancellation.
A quantitative comparison of various classes of oscillators (integrate-and-fire, Winfree, and Kuramoto-Daido type) is performed in the weak-coupling limit for a fully connected network of identical units. An almost perfect agreement is found, with only tiny differences among the models. We also show that the regime of self-consistent partial synchronization is rather general and can be observed for arbitrarily small coupling strength in any model class. As a byproduct of our study, we are able to show that an integrate-and-fire model with a generic pulse shape can be always transformed into a similar model with delta pulses and a suitable phase response curve.
We analyze quasiperiodic partially synchronous states in an ensemble of Stuart-Landau oscillators with global nonlinear coupling. We reveal two types of such dynamics: in the first case the time-averaged frequencies of oscillators and of the mean field differ, while in the second case they are equal, but the motion of oscillators is additionally modulated. We describe transitions from the synchronous state to both types of quasiperiodic dynamics, and a transition between two different quasiperiodic states. We present an example of a bifurcation diagram, where we show the borderlines for all these transitions, as well as domain of bistability.
In this paper, we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches. (c) 2015 AIP Publishing LLC.