Generalized synchronization in relay systems with instantaneous coupling

We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it.

Experimentally determined chaotic phase synchronization in a neuronal system

Mathematical analysis of the subthreshold oscillatory properties of inferior olivary neurons in vitro indicates that the oscillation is nonlinear and supports low dimensional chaotic dynamics. This property leads to the generation of complex functional states that can be attained rapidly via phase coherence that conform to the category of “generalized synchronization.” Functionally, this translates into neuronal ensemble properties that can support maximum functional permissiveness and that rapidly can transform into robustly determined multicellular coherence.

Collective Almost Synchronisation in Complex Networks

This work introduces the phenomenon of Collective Almost Synchronisation (CAS), which describes a universal way of how patterns can appear in complex networks for small coupling strengths. The CAS phenomenon appears due to the existence of an approximately constant local mean field and is characterised by having nodes with trajectories evolving around periodic stable orbits. Common notion based on statistical knowledge would lead one to interpret the appearance of a local constant mean field as a consequence of the fact that the behaviour of each node is not correlated to the behaviours of the others. Contrary to this common notion, we show that various well known weaker forms of synchronisation (almost, time-lag, phase synchronisation, and generalised synchronisation) appear as a result of the onset of an almost constant local mean field. If the memory is formed in a brain by minimising the coupling strength among neurons and maximising the number of possible patterns, then the CAS phenomenon is a plausible explanation for it.

Generalized-positioning for mixed-frequency of mixed-GNSS and its preliminary applications

Modernized GPS and GLONASS, together with new GNSS systems, BeiDou and Galileo, offer code and phase ranging signals in three or more carriers. Traditionally, dual-frequency code and/or phase GPS measurements are linearly combined to eliminate effects of ionosphere delays in various positioning and analysis. This typical treatment method has imitations in processing signals at three or more frequencies from more than one system and can be hardly adapted itself to cope with the booming of various receivers with a broad variety of singles. In this contribution, a generalized-positioning model that the navigation system independent and the carrier number unrelated is promoted, which is suitable for both single- and multi-sites data processing. For the synchronization of different signals, uncalibrated signal delays (USD) are more generally defined to compensate the signal specific offsets in code and phase signals respectively. In addition, the ionospheric delays are included in the parameterization with an elaborate consideration. Based on the analysis of the algebraic structures, this generalized-positioning model is further refined with a set of proper constrains to regularize the datum deficiency of the observation equation system. With this new model, uncalibrated signal delays (USD) and ionospheric delays are derived for both GPS and BeiDou with a large dada set. Numerical results demonstrate that, with a limited number of stations, the uncalibrated code delays (UCD) are determinate to a precision of about 0.1 ns for GPS and 0.4 ns for BeiDou signals, while the uncalibrated phase delays (UPD) for L1 and L2 are generated with 37 stations evenly distributed in China for GPS with a consistency of about 0.3 cycle. Extra experiments concerning the performance of this novel model in point positioning with mixed-frequencies of mixed-constellations is analyzed, in which the USD parameters are fixed with our generated values. The results are evaluated in terms of both positioning accuracy and convergence time.

Generalized vector control for brushless doubly fed machines with nested-loop rotor

This paper presents a generalized vector control system for a generic brushless doubly fed (induction) machine (BDFM) with nested-loop type rotor. The generic BDFM consists of p1/p2 pole-pair stator windings and a nested-loop rotor with N number of loops per nest. The vector control system is derived based on the basic BDFM equation in the synchronous mode accompanied with an appropriate synchronization approach to the grid. An analysis is performed for the vector control system using the generic BDFM vector model. The analysis proves the efficacy of the proposed approach in BDFM electromagnetic torque and rotor flux control. In fact, in the proposed vector control system, the BDFM torque can be controlled very effectively promising a high-performance BDFM shaft speed control system. A closed-loop shaft speed control system is composed based on the presented vector control system whose performance is examined both in simulations and experiments. The results confirm the high performance of the proposed approach in BDFM shaft speed control as well as a very close agreement between the simulations and experiments. Tests are performed on a 180-frame prototype BDFM. © 2012 IEEE.

Synchronization with partial state feedback on SO(n)

In this paper we consider the problem of constructing a distributed feedback law to achieve synchronization for a group of k agents whose states evolve on SO(n) and which exchange only partial state information along communication links. The partial state information is given by the action of the state on reference vectors in ℝn. We propose a gradient based control law which achieves exponential local convergence to a synchronization configuration under a rank condition on a generalized Laplacian matrix. Furthermore, we discuss the case of time-varying reference vectors and provide a convergence result for this case. The latter helps reach synchronization, requiring less communication links and weaker conditions on the instantaneous reference vectors. Our methods are illustrated on an attitude synchronization problem where agents exchange only their relative positions observed in the respective body frames. ©2009 IEEE.

Synchrotron X-ray interlaced microbeams suppress paroxysmal oscillations in neuronal networks initiating generalized epilepsy

Radiotherapy has shown some efficacy for epilepsies but the insufficient confinement of the radiation dose to the pathological target reduces its indications. Synchrotron-generated X-rays overcome this limitation and allow the delivery of focalized radiation doses to discrete brain volumes via interlaced arrays of microbeams (IntMRT). Here, we used IntMRT to target brain structures involved in seizure generation in a rat model of absence epilepsy (GAERS). We addressed the issue of whether and how synchrotron radiotherapeutic treatment suppresses epileptic activities in neuronal networks. IntMRT was used to target the somatosensory cortex (S1Cx), a region involved in seizure generation in the GAERS. The antiepileptic mechanisms were investigated by recording multisite local-field potentials and the intracellular activity of irradiated S1Cx pyramidal neurons in vivo. MRI and histopathological images displayed precise and sharp dose deposition and revealed no impairment of surrounding tissues. Local-field potentials from behaving animals demonstrated a quasi-total abolition of epileptiform activities within the target. The irradiated S1Cx was unable to initiate seizures, whereas neighboring non-irradiated cortical and thalamic regions could still produce pathological oscillations. In vivo intracellular recordings showed that irradiated pyramidal neurons were strongly hyperpolarized and displayed a decreased excitability and a reduction of spontaneous synaptic activities. These functional alterations explain the suppression of large-scale synchronization within irradiated cortical networks. Our work provides the first post-irradiation electrophysiological recordings of individual neurons. Altogether, our data are a critical step towards understanding how X-ray radiation impacts neuronal physiology and epileptogenic processes.

Cortical local and long-range synchronization interplay in human absence seizure initiation

Brain activity relies on transient, fluctuating interactions between segregated neuronal populations. Synchronization within a single and between distributed neuronal clusters reflects the dynamics of these cooperative patterns. Thus absence epilepsy can be used as a model for integrated, large-scale investigation of the emergence of pathological collective dynamics in the brain. Indeed, spike-wave discharges (SWD) of an absence seizure are thought to reflect abnormal cortical hypersynchronization. In this paper, we address two questions: how and where do SWD arise in the human brain? Therefore, we explored the spatio-temporal dynamics of interactions within and between widely distributed cortical sites using magneto-encephalographic recordings of spontaneous absence seizures. We then extracted, from their time-frequency analysis, local synchronization of cortical sources and long-range synchronization linking distant sites. Our analyses revealed a reproducible sequence of 1) long-range desynchronization, 2) increased local synchronization and 3) increased long-range synchronization. Although both local and long-range synchronization displayed different spatio-temporal profiles, their cortical projection within an initiation time window overlap and reveal a multifocal fronto-central network. These observations contradict the classical view of sudden generalized synchronous activities in absence epilepsy. Furthermore, they suggest that brain states transition may rely on multi-scale processes involving both local and distant interactions.

Synchronization processes in nonlinear systems and their relation to cortical oscillatory dynamics

This thesis was focused on theoretical models of synchronization to cortical dynamics as measured by magnetoencephalography (MEG). Dynamical systems theory was used in both identifying relevant variables for brain coordination and also in devising methods for their quantification. We presented a method for studying interactions of linear and chaotic neuronal sources using MEG beamforming techniques. We showed that such sources can be accurately reconstructed in terms of their location, temporal dynamics and possible interactions. Synchronization in low-dimensional nonlinear systems was studied to explore specific correlates of functional integration and segregation. In the case of interacting dissimilar systems, relevant coordination phenomena involved generalized and phase synchronization, which were often intermittent. Spatially-extended systems were then studied. For locally-coupled dissimilar systems, as in the case of cortical columns, clustering behaviour occurred. Synchronized clusters emerged at different frequencies and their boundaries were marked through oscillation death. The macroscopic mean field revealed sharp spectral peaks at the frequencies of the clusters and broader spectral drops at their boundaries. These results question existing models of Event Related Synchronization and Desynchronization. We re-examined the concept of the steady-state evoked response following an AM stimulus. We showed that very little variability in the AM following response could be accounted by system noise. We presented a methodology for detecting local and global nonlinear interactions from MEG data in order to account for residual variability. We found crosshemispheric nonlinear interactions of ongoing cortical rhythms concurrent with the stimulus and interactions of these rhythms with the following AM responses. Finally, we hypothesized that holistic spatial stimuli would be accompanied by the emergence of clusters in primary visual cortex resulting in frequency-specific MEG oscillations. Indeed, we found different frequency distributions in induced gamma oscillations for different spatial stimuli, which was suggestive of temporal coding of these spatial stimuli. Further, we addressed the bursting character of these oscillations, which was suggestive of intermittent nonlinear dynamics. However, we did not observe the characteristic-3/2 power-law scaling in the distribution of interburst intervals. Further, this distribution was only seldom significantly different to the one obtained in surrogate data, where nonlinear structure was destroyed. In conclusion, the work presented in this thesis suggests that advances in dynamical systems theory in conjunction with developments in magnetoencephalography may facilitate a mapping between levels of description int he brain. this may potentially represent a major advancement in neuroscience.