Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSuppression of synchronous spiking in two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons
85
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Collective oscillations and their suppression by external stimulation are analyzed in a large-scale neural network consisting of two interacting populations of excitatory and inhibitory quadratic integrate-and-fire neurons. In the limit of an infinite number of neurons, the microscopic model of this network can be reduced to an exact low-dimensional system of mean-field equations. Bifurcation analysis of these equations reveals three different dynamic modes in a free network: a stable resting state, a stable limit cycle, and bistability with a coexisting resting state and a limit cycle. We show that in the limit cycle mode, high-frequency stimulation of an inhibitory population can stabilize an unstable resting state and effectively suppress collective oscillations. We also show that in the bistable mode, the dynamics of the network can be switched from a stable limit cycle to a stable resting state by applying an inhibitory pulse to the excitatory population. The results obtained from the mean-field equations are confirmed by numerical simulation of the microscopic model.
rate research
Read More
We analyze the dynamics of two coupled identical populations of quadratic integrate-and-fire neurons, which represent the canonical model for class I neurons near the spiking threshold. The populations are heterogeneous; they include both inherently spiking and excitable neurons. The coupling within and between the populations is global via synapses that take into account the finite width of synaptic pulses. Using a recently developed reduction method based on the Lorentzian ansatz, we derive a closed system of equations for the neurons firing rates and the mean membrane potentials in both populations. The reduced equations are exact in the infinite-size limit. The bifurcation analysis of the equations reveals a rich variety of non-symmetric patterns, including a splay state, antiphase periodic oscillations, chimera-like states, also chaotic oscillations as well as bistabilities between various states. The validity of the reduced equations is confirmed by direct numerical simulations of the finite-size networks.
A companion paper introduces a nonlinear network with Hebbian excitatory (E) neurons that are reciprocally coupled with anti-Hebbian inhibitory (I) neurons and also receive Hebbian feedforward excitation from sensory (S) afferents. The present paper derives the network from two normative principles that are mathematically equivalent but conceptually different. The first principle formulates unsupervised learning as a constrained optimization problem: maximization of S-E correlations subject to a copositivity constraint on E-E correlations. A combination of Legendre and Lagrangian duality yields a zero-sum continuous game between excitatory and inhibitory connections that is solved by the neural network. The second principle defines a zero-sum game between E and I cells. E cells want to maximize S-E correlations and minimize E-I correlations, while I cells want to maximize I-E correlations and minimize power. The conflict between I and E objectives effectively forces the E cells to decorrelate from each other, although only incompletely. Legendre duality yields the neural network.
Dynamic excitatory-inhibitory (E-I) balance is a paradigmatic mechanism invoked to explain the irregular low firing activity observed in the cortex. However, we will show that the E-I balance can be at the origin of other regimes observable in the brain. The analysis is performed by combining simulations of sparse E-I networks composed of N spiking neurons with analytical investigations of low dimensional neural mass models. The bifurcation diagrams, derived for the neural mass model, allow to classify the asynchronous and coherent behaviours emerging any finite in-degree K. In the limit N >> K >> 1 both supra and sub-threshold balanced asynchronous regimes can be observed. Due to structural heterogeneity the asynchronous states are characterized by the splitting of the neurons in three groups: silent, fluctuation and mean driven. The coherent rhythms are characterized by regular or irregular temporal fluctuations joined to spatial coherence similar to coherent fluctuations observed in the cortex over multiple spatial scales. Collective Oscillations (COs) can emerge due to two different mechanisms. A first mechanism similar to the pyramidal-interneuron gamma (PING) one. The second mechanism is intimately related to the presence of current fluctuations, which sustain COs characterized by an essentially simultaneous bursting of the two populations. We observe period-doubling cascades involving the PING-like COs finally leading to the appearance of coherent chaos. For sufficiently strong current fluctuations we report a novel mechanism of frequency locking among collective rhythms promoted by these intrinsic fluctuations. Our analysis suggest that despite PING-like or fluctuation driven COS are observable for any finite in-degree K, in the limit N >> K >> 1 these solutions result in two coexisting balanced regimes: an asynchronous and a fully synchronized one.
Oscillations are a hallmark of neural population activity in various brain regions with a spectrum covering a wide range of frequencies. Within this spectrum gamma oscillations have received particular attention due to their ubiquitous nature and to their correlation with higher brain functions. Recently, it has been reported that gamma oscillations in the hippocampus of behaving rodents are segregated in two distinct frequency bands: slow and fast. These two gamma rhythms correspond to dfferent states of the network, but their origin has been not yet clarified. Here, we show theoretically and numerically that a single inhibitory population can give rise to coexisting slow and fast gamma rhythms corresponding to collective oscillations of a balanced spiking network. The slow and fast gamma rhythms are generated via two different mechanisms: the fast one being driven by the coordinated tonic neural firing and the slow one by endogenous fluctuations due to irregular neural activity. We show that almost instantaneous stimulations can switch the collective gamma oscillations from slow to fast and vice versa. Furthermore, to make a closer contact with the experimental observations, we consider the modulation of the gamma rhythms induced by a slower (theta) rhythm driving the network dynamics. In this context, depending on the strength of the forcing, we observe phase-amplitude and phase-phase coupling between the fast and slow gamma oscillations and the theta forcing. Phase-phase coupling reveals different theta-phases preferences for the two coexisting gamma rhythms.
We derive analytical formulae for the firing rate of integrate-and-fire neurons endowed with realistic synaptic dynamics. In particular we include the possibility of multiple synaptic inputs as well as the effect of an absolute refractory period into the description.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
