432 research outputs found
Synchronization of electrically coupled resonate-and-fire neurons
Electrical coupling between neurons is broadly present across brain areas and
is typically assumed to synchronize network activity. However, intrinsic
properties of the coupled cells can complicate this simple picture. Many cell
types with strong electrical coupling have been shown to exhibit resonant
properties, and the subthreshold fluctuations arising from resonance are
transmitted through electrical synapses in addition to action potentials. Using
the theory of weakly coupled oscillators, we explore the effect of both
subthreshold and spike-mediated coupling on synchrony in small networks of
electrically coupled resonate-and-fire neurons, a hybrid neuron model with
linear subthreshold dynamics and discrete post-spike reset. We calculate the
phase response curve using an extension of the adjoint method that accounts for
the discontinuity in the dynamics. We find that both spikes and resonant
subthreshold fluctuations can jointly promote synchronization. The subthreshold
contribution is strongest when the voltage exhibits a significant post-spike
elevation in voltage, or plateau. Additionally, we show that the geometry of
trajectories approaching the spiking threshold causes a "reset-induced shear"
effect that can oppose synchrony in the presence of network asymmetry, despite
having no effect on the phase-locking of symmetrically coupled pairs
Spiking Dynamics during Perceptual Grouping in the Laminar Circuits of Visual Cortex
Grouping of collinear boundary contours is a fundamental process during visual perception. Illusory contour completion vividly illustrates how stable perceptual boundaries interpolate between pairs of contour inducers, but do not extrapolate from a single inducer. Neural models have simulated how perceptual grouping occurs in laminar visual cortical circuits. These models predicted the existence of grouping cells that obey a bipole property whereby grouping can occur inwardly between pairs or greater numbers of similarly oriented and co-axial inducers, but not outwardly from individual inducers. These models have not, however, incorporated spiking dynamics. Perceptual grouping is a challenge for spiking cells because its properties of collinear facilitation and analog sensitivity to inducer configurations occur despite irregularities in spike timing across all the interacting cells. Other models have demonstrated spiking dynamics in laminar neocortical circuits, but not how perceptual grouping occurs. The current model begins to unify these two modeling streams by implementing a laminar cortical network of spiking cells whose intracellular temporal dynamics interact with recurrent intercellular spiking interactions to quantitatively simulate data from neurophysiological experiments about perceptual grouping, the structure of non-classical visual receptive fields, and gamma oscillations.CELEST, an NSF Science of Learning Center (SBE-0354378); SyNAPSE program of the Defense Advanced Research Project Agency (HR001109-03-0001); Defense Advanced Research Project Agency (HR001-09-C-0011
PRINCIPLES OF INFORMATION PROCESSING IN NEURONAL AVALANCHES
How the brain processes information is poorly understood. It has been suggested that the imbalance of excitation and inhibition (E/I) can significantly affect information processing in the brain. Neuronal avalanches, a type of spontaneous activity recently discovered, have been ubiquitously observed in vitro and in vivo when the cortical network is in the E/I balanced state. In this dissertation, I experimentally demonstrate that several properties regarding information processing in the cortex, i.e. the entropy of spontaneous activity, the information transmission between stimulus and response, the diversity of synchronized states and the discrimination of external stimuli, are optimized when the cortical network is in the E/I balanced state, exhibiting neuronal avalanche dynamics. These experimental studies not only support the hypothesis that the cortex operates in the critical state, but also suggest that criticality is a potential principle of information processing in the cortex. Further, we study the interaction structure in population neuronal dynamics, and discovered a special structure of higher order interactions that are inherent in the neuronal dynamics
Scale-free avalanches in arrays of FitzHugh-Nagumo oscillators
The activity in the brain cortex remarkably shows a simultaneous presence of
robust collective oscillations and neuronal avalanches, where intermittent
bursts of pseudo-synchronous spiking are interspersed with long periods of
quiescence. The mechanisms allowing for such a coexistence are still a matter
of an intensive debate. Here, we demonstrate that avalanche activity patterns
can emerge in a rather simple model of an array of diffusively coupled neural
oscillators with multiple timescale local dynamics in vicinity of a canard
transition. The avalanches coexist with the fully synchronous state where the
units perform relaxation oscillations. We show that the mechanism behind the
avalanches is based on an inhibitory effect of interactions, which may quench
the spiking of units due to an interplay with the maximal canard. The avalanche
activity bears certain heralds of criticality, including scale-invariant
distributions of event sizes. Furthermore, the system shows an increased
sensitivity to perturbations, manifested as critical slowing down and a reduced
resilience.Comment: 9 figure
Mathematical frameworks for oscillatory network dynamics in neuroscience
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear—for example, heteroclinic network attractors. In this review we present a set of mathemat- ical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical frame- work for further successful applications of mathematics to understanding network dynamics in neuroscience
Synchronous chaos and broad band gamma rhythm in a minimal multi-layer model of primary visual cortex
Visually induced neuronal activity in V1 displays a marked gamma-band
component which is modulated by stimulus properties. It has been argued that
synchronized oscillations contribute to these gamma-band activity [...
however,] even when oscillations are observed, they undergo temporal
decorrelation over very few cycles. This is not easily accounted for in
previous network modeling of gamma oscillations. We argue here that
interactions between cortical layers can be responsible for this fast
decorrelation. We study a model of a V1 hypercolumn, embedding a simplified
description of the multi-layered structure of the cortex. When the stimulus
contrast is low, the induced activity is only weakly synchronous and the
network resonates transiently without developing collective oscillations. When
the contrast is high, on the other hand, the induced activity undergoes
synchronous oscillations with an irregular spatiotemporal structure expressing
a synchronous chaotic state. As a consequence the population activity undergoes
fast temporal decorrelation, with concomitant rapid damping of the oscillations
in LFPs autocorrelograms and peak broadening in LFPs power spectra. [...]
Finally, we argue that the mechanism underlying the emergence of synchronous
chaos in our model is in fact very general. It stems from the fact that gamma
oscillations induced by local delayed inhibition tend to develop chaos when
coupled by sufficiently strong excitation.Comment: 49 pages, 11 figures, 7 table
Synchrony and bifurcations in coupled dynamical systems and effects of time delay
Dynamik auf Netzwerken ist ein mathematisches Feld, das in den letzten Jahrzehnten schnell gewachsen ist und Anwendungen in zahlreichen Disziplinen wie z.B. Physik, Biologie und Soziologie findet. Die Funktion vieler Netzwerke hängt von der Fähigkeit ab, die Elemente des Netzwerkes zu synchronisieren. Mit anderen Worten, die Existenz und die transversale Stabilität der synchronen Mannigfaltigkeit sind zentrale Eigenschaften. Erst seit einigen Jahren wird versucht, den verwickelten Zusammenhang zwischen der Kopplungsstruktur und den Stabilitätseigenschaften synchroner Zustände zu verstehen. Genau das ist das zentrale Thema dieser Arbeit. Zunächst präsentiere ich erste Ergebnisse zur Klassifizierung der Kanten eines gerichteten Netzwerks bezüglich ihrer Bedeutung für die Stabilität des synchronen Zustands. Folgend untersuche ich ein komplexes Verzweigungsszenario in einem gerichteten Ring von Stuart-Landau Oszillatoren und zeige, dass das Szenario persistent ist, wenn dem Netzwerk eine schwach gewichtete Kante hinzugefügt wird. Daraufhin untersuche ich synchrone Zustände in Ringen von Phasenoszillatoren die mit Zeitverzögerung gekoppelt sind. Ich bespreche die Koexistenz synchroner Lösungen und analysiere deren Stabilität und Verzweigungen. Weiter zeige ich, dass eine Zeitverschiebung genutzt werden kann, um Muster im Ring zu speichern und wiederzuerkennen. Diese Zeitverschiebung untersuche ich daraufhin für beliebige Kopplungsstrukturen. Ich zeige, dass invariante Mannigfaltigkeiten des Flusses sowie ihre Stabilität unter der Zeitverschiebung erhalten bleiben. Darüber hinaus bestimme ich die minimale Anzahl von Zeitverzögerungen, die gebraucht werden, um das System äquivalent zu beschreiben. Schließlich untersuche ich das auffällige Phänomen eines nichtstetigen Übergangs zu Synchronizität in Klassen großer Zufallsnetzwerke indem ich einen kürzlich eingeführten Zugang zur Beschreibung großer Zufallsnetzwerke auf den Fall zeitverzögerter Kopplungen verallgemeinere.Since a couple of decades, dynamics on networks is a rapidly growing branch of mathematics with applications in various disciplines such as physics, biology or sociology. The functioning of many networks heavily relies on the ability to synchronize the network’s nodes. More precisely, the existence and the transverse stability of the synchronous manifold are essential properties. It was only in the last few years that people tried to understand the entangled relation between the coupling structure of a network, given by a (di-)graph, and the stability properties of synchronous states. This is the central theme of this dissertation. I first present results towards a classification of the links in a directed, diffusive network according to their impact on the stability of synchronization. Then I investigate a complex bifurcation scenario observed in a directed ring of Stuart-Landau oscillators. I show that under the addition of a single weak link, this scenario is persistent. Subsequently, I investigate synchronous patterns in a directed ring of phase oscillators coupled with time delay. I discuss the coexistence of multiple of synchronous solutions and investigate their stability and bifurcations. I apply these results by showing that a certain time-shift transformation can be used in order to employ the ring as a pattern recognition device. Next, I investigate the same time-shift transformation for arbitrary coupling structures in a very general setting. I show that invariant manifolds of the flow together with their stability properties are conserved under the time-shift transformation. Furthermore, I determine the minimal number of delays needed to equivalently describe the system’s dynamics. Finally, I investigate a peculiar phenomenon of non-continuous transition to synchrony observed in certain classes of large random networks, generalizing a recently introduced approach for the description of large random networks to the case of delayed couplings
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