Macroscopic self-oscillations and aging transition in a network of synaptically coupled quadratic integrate-and-fire neurons

Ratas, Irmantas; Pyragas, K.

doi:10.1103/physreve.94.032215

Cited by 50 publications

(49 citation statements)

References 35 publications

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“…As proved recently [38], NFMs with time-scale separation display a rich variety of robust spatio-temporal patterns, which may also be supported by our model. Also, recent work has been done to extend the local firing rate equations derived in [28] to include synaptic kinetics [39][40][41][42] or fixed delays [43]. These studies all show that time delays due to synaptic processing generally lead to the emergence of self-sustained oscillations due to collective synchronization.…”

Section: Discussionmentioning

confidence: 99%

Synchrony-induced modes of oscillation of a neural field model

et al. 2017

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We investigate the modes of oscillation of heterogeneous ring networks of quadratic integrate-and-fire (QIF) neurons with nonlocal, space-dependent coupling. Perturbations of the equilibrium state with a particular wave number produce transient standing waves with a specific temporal frequency, analogously to those in a tense string. In the neuronal network, the equilibrium corresponds to a spatially homogeneous, asynchronous state. Perturbations of this state excite the network's oscillatory modes, which reflect the interplay of episodes of synchronous spiking with the excitatory-inhibitory spatial interactions. In the thermodynamic limit, an exact low-dimensional neural field model describing the macroscopic dynamics of the network is derived. This allows us to obtain formulas for the Turing eigenvalues of the spatially homogeneous state and hence to obtain its stability boundary. We find that the frequency of each Turing mode depends on the corresponding Fourier coefficient of the synaptic pattern of connectivity. The decay rate instead is identical for all oscillation modes as a consequence of the heterogeneity-induced desynchronization of the neurons. Finally, we numerically compute the spectrum of spatially inhomogeneous solutions branching from the Turing bifurcation, showing that similar oscillatory modes operate in neural bump states and are maintained away from onset.

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Section: Discussionmentioning

confidence: 99%

Synchrony-induced modes of oscillation of a neural field model

et al. 2017

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“…These regimes could be well traversed via transient inputs, as depicted in Figure 4B. Driving the microscopic model given by (2) and (20)(21)(22)(23) with the same transient inputs, we found that the spiking dynamics were still attracted to the low-dimensional manifold described by the macroscopic system. This shows, that even with τ A = 10τ , the condition τ A τ is sufficiently satisfied for the macroscopic description of the population bursting dynamics to be valid.…”

Section: Ivb Effects Of Sfamentioning

confidence: 79%

“…Forη, the parameter range in which the limit cycle exists corresponds to most of the cells in the population being in an excitable regime and has been reported for a number of models using QIF neurons (e.g. 15,22,23 ). Within this range, the inter-burst period can be varied from 13τ up to 105τ via changes in α andη (see Figure 3B).…”

Section: Iiic Limit Cycle Characteristicsmentioning

confidence: 85%

A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation

Gast

Schmidt

Knösche

2019

Preprint

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Bursting plays an important role in neural communication. At the population level, macroscopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of such phase transitions, mean-field descriptions of macroscopic bursting behavior pose a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons in which collective bursting behavior arises via short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. We characterize the emerging bursting behavior using bifurcation analysis and validate our mean-field derivations by comparing the microscopic and macroscopic descriptions of the population dynamics. Hence, we provide mechanistic descriptions of phase transitions between bursting and non-bursting population dynamics which play important roles in both healthy neural communication and neurological disorders.

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“…Even though the Montbrió model is only a single-population model, it has been shown 620 to have a rich dynamic profile with oscillatory and even bi-stable regimes [38,47] while the frequency of the oscillatory forcing was chosen as ω = π 20 . As shown in Figure 635 3, we were able to replicate the above described model behavior.…”

Section: Montbrió Model 619mentioning

confidence: 99%

“…Even though the Montbrió model is only a single-population model, it has been shown to have a rich dynamic profile with oscillatory and even bi-stable regimes [38,47]. To investigate the response of the model to non-stationary inputs, Montbrió et al initialized the model in a bi-stable dynamic regime and applied (1) constant and (2) sinusoidal extrinsic forcing within a short time-window.…”

Section: Montbrió Modelmentioning

confidence: 99%

PyRates – A Python Framework for rate-based neural Simulations

Gast

Rose

Moeller

et al. 2019

Preprint

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In neuroscience, computational modeling has become an important source of insight into brain states and dynamics. A basic requirement for computational modeling studies is the availability of efficient software for setting up models and performing numerical simulations. While many such tools exist for different families of neural models, there is a lack of tools allowing for both a generic model definition and efficiently parallelized simulations. In this work, we present PyRates, a Python framework that provides the means to build a large variety of neural models as a graph. PyRates provides intuitive access to and modification of all mathematical operators in a graph, thus allowing for a highly generic model definition. For computational efficiency and parallelization, the model graph is translated into a tensorflow-based compute graph. Using the example of two different neural models belonging to the family of rate-based population models, we explain the mathematical formalism, software structure and user interfaces of PyRates. We then show via numerical simulations that the behavior shown by the model implementations in PyRates is consistent with the literature. Finally, we demonstrate the computational capacities and scalability of PyRates via a number of benchmark simulations of neural networks differing in size and connectivity.

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Macroscopic self-oscillations and aging transition in a network of synaptically coupled quadratic integrate-and-fire neurons

Cited by 50 publications

References 35 publications

Synchrony-induced modes of oscillation of a neural field model

Synchrony-induced modes of oscillation of a neural field model

A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation

PyRates – A Python Framework for rate-based neural Simulations

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