277 research outputs found

    Scale-free avalanches in arrays of FitzHugh-Nagumo oscillators

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    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

    Collective Activity Bursting in a Population of Excitable Units Adaptively Coupled to a Pool of Resources

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    We study the collective dynamics in a population of excitable units (neurons) adaptively interacting with a pool of resources. The resource pool is influenced by the average activity of the population, whereas the feedback from the resources to the population is comprised of components acting homogeneously or inhomogeneously on individual units of the population. Moreover, the resource pool dynamics is assumed to be slow and has an oscillatory degree of freedom. We show that the feedback loop between the population and the resources can give rise to collective activity bursting in the population. To explain the mechanisms behind this emergent phenomenon, we combine the Ott-Antonsen reduction for the collective dynamics of the population and singular perturbation theory to obtain a reduced system describing the interaction between the population mean field and the resources.Peer Reviewe

    Storage of phase-coded patterns via STDP in fully-connected and sparse network: a study of the network capacity

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    We study the storage and retrieval of phase-coded patterns as stable dynamical attractors in recurrent neural networks, for both an analog and a integrate-and-fire spiking model. The synaptic strength is determined by a learning rule based on spike-time-dependent plasticity, with an asymmetric time window depending on the relative timing between pre- and post-synaptic activity. We store multiple patterns and study the network capacity. For the analog model, we find that the network capacity scales linearly with the network size, and that both capacity and the oscillation frequency of the retrieval state depend on the asymmetry of the learning time window. In addition to fully-connected networks, we study sparse networks, where each neuron is connected only to a small number z << N of other neurons. Connections can be short range, between neighboring neurons placed on a regular lattice, or long range, between randomly chosen pairs of neurons. We find that a small fraction of long range connections is able to amplify the capacity of the network. This imply that a small-world-network topology is optimal, as a compromise between the cost of long range connections and the capacity increase. Also in the spiking integrate and fire model the crucial result of storing and retrieval of multiple phase-coded patterns is observed. The capacity of the fully-connected spiking network is investigated, together with the relation between oscillation frequency of retrieval state and window asymmetry

    Metastability, Criticality and Phase Transitions in brain and its Models

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    This essay extends the previously deposited paper "Oscillations, Metastability and Phase Transitions" to incorporate the theory of Self-organizing Criticality. The twin concepts of Scaling and Universality of the theory of nonequilibrium phase transitions is applied to the role of reentrant activity in neural circuits of cerebral cortex and subcortical neural structures

    Criticality and its effect on other cortical phenomena

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    Neuronal avalanches are a cortical phenomenon defined by bursts of neuronal firing encapsulated by periods of quiescence. It has been found both in vivo and in vitro that neuronal avalanches follow a power law distribution which is indicative of the system being within or near a critical state. A system is critical if it is poised between order and disorder with the possibility of minor event leading to a large chain reaction. This is also observed by the system exhibiting a diverging correlation length between its components as it approaches the critical point. It has been shown that neuronal criticality is a scale-free phenomenon observed throughout the entire system as well as within each module of the system. At a small scale, neuronal networks produce avalanches which conform to power law-like distributions. At a larger scale, we observe that these systems consist of modules exhibiting long-range temporal correlations identifiable via Detrended Fluctuation Analysis (DFA). This phenomenon is hypothesised to affect network behaviour with regards to information processing, information storage, computational power, and stability - The Criticality Hypothesis. This thesis attempts to better understand critical neuronal networks and how criticality may link with other neuronal phenomena. This work begins by investigating the interplay of network connectivity, synaptic plasticity, and criticality. Using different network construction algorithms, the thesis demonstrates that Hebbian learning and Spike Timing Dependent Plasticity (STDP) robustly drive small networks towards a critical state. Moreover the thesis shows that, while the initial distribution of synaptic weights plays a significant role in attaining criticality, the network's topology at the modular level has little or no impact. Using an expanded eight-module oscillatory spiking neural network the thesis then shows the link between the different critical markers we use when attempting to observe critical behaviour at different scales. The findings demonstrate that modules exhibiting power law-like behaviour also demonstrate long-range temporal correlations throughout the system. Furthermore, we show that when modules no longer exhibit power law-like behaviour we find that they become uncorrelated or noisy. This shows a correlation between power law-like behaviour observed within each module and the long-range temporal correlations between the modules. The thesis concludes by demonstrating how criticality may be linked with other related phenomena, namely metastability and dynamical complexity. Metastability is a global property of neuronal populations that migrate between attractor-like states. Metastability can be quantified by the variance of synchrony, a measure that has been hypothesised to capture the varying influence neuronal populations have over one another and the system as a whole. The thesis shows a correlation between critical behaviour and metastability where the latter is most reliably maximised only when the former is near the critical state. This conclusion is expected as metastability, similarly to criticality reflects the interplay between the integrating and segregating tendencies of the system components. Agreeing with previous findings this suggests that metastable dynamics may be another marker of critical behaviour. A neural system is said to exhibit dynamical complexity if a balance of integrated and segregated activity occurs within the system. A common attribute of critical systems is a balance between excitation and inhibition. The final part of the thesis attempts to understand how criticality may be linked with dynamical complexity. This work shows a possible connection between these phenomena providing a foundation for further analysis. The thesis concludes with a discussion of the significant role criticality plays in determining the behaviour of neuronal networks.Open Acces

    Self-sustained irregular activity in an ensemble of neural oscillators

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    An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is observed. The "synchronised phase", which emerges upon increasing the coupling strength, is characterized by highly-irregular fluctuations: a time-series analysis reveals that the dynamics of the order parameter is indeed high-dimensional. The complex dynamics appears to be the result of the non-perturbative action of a suitably shaped phase-response curve. Such mechanism differs from the often invoked balance between excitation and inhibition and might provide an alternative basis to account for the self-sustained brain activity in the resting state. The potential interest of this dynamical regime is further strengthened by its (microscopic) linear stability, which makes it quite suited for computational tasks. The overall study has been performed by combining analytical and numerical studies, starting from the linear stability analysis of the asynchronous regime, to include the Fourier analysis of the Kuramoto order parameter, the computation of various types of Lyapunov exponents, and a microscopic study of the inter-spike intervals.Comment: 11 pages, 10 figure
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