In this paper, we introduce a modification of a mean-field model used to describe the brain's electrical activity as recorded via electroencephalography (EEG). The focus of the present study is to understand the mechanisms giving rise to the dynamics observed during absence epilepsy, one of the classical generalized syndromes. A systematic study of the data from a number of different subjects with absence epilepsy demonstrates a wide variety of dynamical phenomena in the recorded EEG. In addition to the classical spike and wave activity, there may be polyspike and wave, wave spike or even no discernible spike-wave onset during seizure events. The model we introduce is able to capture all of these different phenomena and we describe the bifurcations giving rise to these different types of seizure activity. We argue that such a model may provide a useful clinical tool for classifying different subclasses of absence epilepsy.
In this paper we describe how an ordinary differential equation model of corticothalamic interactions may be obtained from a more general system of delay differential equations. We demonstrate that transitions to epileptic dynamics via changes in system parameters are qualitatively the same as in the original model with delay, as well as demonstrating that the onset of epileptic activity may arise due to regions of bistability. Hence, the model presents in one unique framework, two competing theories for the genesis of epileptiform activity. Similarities between model transitions and clinical data are presented and we argue that statistics obtained from, and a parameter estimation of this model may be a potential means of classifying and predicting the onset and offset of seizure activity.
form only given. This work discusses the technical and economical benefits of different active and reactive power control strategies for grid-connected photovoltaic systems in Germany. The aim of these control strategies is to limit the voltage rise, caused by a high local photovoltaic power feed-in and hence allow additional photovoltaic capacity to be connected to the mains. Autonomous inverter control strategies, which do not require any kind of data communication between the inverter and its environment, as well as an on-load tap changer for distribution transformers is investigated. The technical and economical assessment of these strategies is derived from 12 month RMS simulations, which are based on a real low voltage grid and measured DC power generation values. The results show that the provision of reactive power is an especially effective way to increase the hosting capacity of a low voltage grid for photovoltaic systems
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