# Collective irregular dynamics in balanced networks of leaky integrate-and-fire neurons

@article{Politi2018CollectiveID, title={Collective irregular dynamics in balanced networks of leaky integrate-and-fire neurons}, author={Antonio Politi and Ekkehard Ullner and Alessandro Torcini}, journal={The European Physical Journal Special Topics}, year={2018}, volume={227}, pages={1185-1204} }

Abstract
We extensively explore networks of weakly unbalanced, leaky integrate-and-fire (LIF) neurons for different coupling strength, connectivity, and by varying the degree of refractoriness, as well as the delay in the spike transmission. We find that the neural network does not only exhibit a microscopic (single-neuron) stochastic-like evolution, but also a collective irregular dynamics (CID). Our analysis is based on the computation of a suitable order parameter, typically used to…

## Figures and Tables from this paper

## 21 Citations

Ubiquity of collective irregular dynamics in balanced networks of spiking neurons.

- Medicine, PhysicsChaos
- 2018

A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition prevails, the asymptotic regime is not asynchronous but rather characterized by a self-sustained irregular, macroscopic (collective) dynamics.

Asynchronous and Coherent Dynamics in Balanced Excitatory-Inhibitory Spiking Networks

- Biology, PhysicsFrontiers in Systems Neuroscience
- 2021

It is shown that the E-I balance can be at the origin of other regimes observable in the brain, including period-doubling cascades involving the PING-like COs finally leading to the appearance of coherent chaos.

Collective dynamics in the presence of finite-width pulses.

- Medicine, PhysicsChaos
- 2021

A robust collective irregular dynamics is found, which collapses onto a fully synchronous regime if the inhibitory pulses are sufficiently wider than the excitatory ones and the transition to synchrony is accompanied by hysteretic phenomena.

Quantitative and qualitative analysis of asynchronous neural activity

- Sociology, Physics
- 2019

The activity of a sparse network of leaky integrate-and-fire neurons is carefully revisited with reference to a regime of a bona-fide asynchronous dynamics, and the distribution of interspike intervals turns out to be relatively long-tailed; a crucial feature required for the self-sustainment of the bursting activity in a regime where neurons operate on average (much) below threshold.

Dynamics of a network of quadratic integrate-and-fire neurons with bimodal heterogeneity

- PhysicsPhysics Letters A
- 2021

An exact low-dimensional system of mean-field equations for an infinite-size network of pulse coupled integrate-and-fire neurons with a bimodal distribution of an excitability parameter is derived.…

Asynchronous and coherent dynamics in balanced excitatory-inhibitory populations

- Biology
- 2021

The analysis suggests that despite PING-like or fluctuation driven COS are observable for any finite in-degree K, in the limit N >> K >> 1 these solutions finally result in two coexisting balanced regimes: an asynchronous and a fully synchronized one.

The effect of pulse width on the dynamics of pulse-coupled oscillators

- Biology, Mathematics
- 2021

A robust collective irregular dynamics is found, which collapses onto a fully synchronous regime if the inhibitory pulses are sufficiently wider than the excitatory ones and the transition to synchrony is accompanied by hysteretic phenomena.

Neural activity of heterogeneous inhibitory spiking networks with delay.

- Medicine, PhysicsPhysical review. E
- 2019

A network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses is studied and for very large inhibition neurons display a bursting behavior alternating periods of silence with periods where they fire freely in absence of any inhibition.

Stability of synchronous states in sparse neuronal networks

- Computer Science
- 2020

A detailed analysis of the stability of synchronous states in the context of two populations of inhibitory and excitatory neurons, characterized by two different pulse-widths, finds that the overall stability depends crucially on the relative pulse- width.

Correlated states in balanced neuronal networks.

- Medicine, Computer SciencePhysical review. E
- 2019

An in-depth analysis of the resulting "correlated state" in balanced networks is provided and it is shown that, unlike the asynchronous state, it produces a tight excitatory-inhibitory balance consistent with in vivo cortical recordings.

## References

SHOWING 1-10 OF 56 REFERENCES

Ubiquity of collective irregular dynamics in balanced networks of spiking neurons.

- Medicine, PhysicsChaos
- 2018

A detailed investigation of the thermodynamic limit for fixed density of connections (massive coupling) shows that, when inhibition prevails, the asymptotic regime is not asynchronous but rather characterized by a self-sustained irregular, macroscopic (collective) dynamics.

Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons

- Computer Science, MedicineJournal of Computational Neuroscience
- 2004

The dynamics of networks of sparsely connected excitatory and inhibitory integrate-and-fire neurons are studied analytically. The analysis reveals a rich repertoire of states, including synchronous…

Slow fluctuations in recurrent networks of spiking neurons.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2015

A transition is found in the long-term variability of a sparse recurrent network of perfect integrate-and-fire neurons at which the Fano factor switches from zero to infinity and the correlation time is minimized, corresponding to a bifurcation in a linear map arising from the self-consistency of temporal input and output statistics.

Irregular collective behavior of heterogeneous neural networks.

- Medicine, BiologyPhysical review letters
- 2010

Numerical simulations of large systems indicate that, at variance with the Kuramoto model, the macroscopic dynamics stays irregular and the microscopic (single-neuron) evolution is linearly stable.

Desynchronization in diluted neural networks.

- Mathematics, MedicinePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2006

The dynamical behavior of a weakly diluted fully inhibitory network of pulse-coupled spiking neurons is investigated, and the paradox is solved by drawing an analogy with the phenomenon of "stable chaos" by observing that the stochasticlike behavior is "limited" to an exponentially long transient.

Two types of asynchronous activity in networks of excitatory and inhibitory spiking neurons

- Computer Science, MedicineNature Neuroscience
- 2014

It is shown that an unstructured, sparsely connected network of model spiking neurons can display two fundamentally different types of asynchronous activity that imply vastly different computational properties.

Chaos in Neuronal Networks with Balanced Excitatory and Inhibitory Activity

- Physics, MedicineScience
- 1996

The hypothesis that the temporal variability in the firing of a neuron results from an approximate balance between its excitatory and inhibitory inputs was investigated theoretically.

Intrinsically-generated fluctuating activity in excitatory-inhibitory networks

- Physics, BiologyPLoS Comput. Biol.
- 2017

It is shown that the presence of excitation qualitatively modifies the fluctuating activity compared to purely inhibitory networks, and that signatures of the second dynamical regime appear in networks of integrate-and-fire neurons.

Stability of the splay state in networks of pulse-coupled neurons

- Physics, MathematicsJournal of mathematical neuroscience
- 2012

It is found that in the case of discontinuous velocity fields, the Floquet spectrum scales as 1/N2 and the stability is determined by the sign of the jump at the discontinuity, and the form of the spectrum depends on the pulse shape, but it is independent of the velocity field.

Self-consistent determination of the spike-train power spectrum in a neural network with sparse connectivity

- Computer Science, MedicineFront. Comput. Neurosci.
- 2014

This work simulates a single neuron over several generations and studies a self-consistent statistics of input and output spectra of neural spike trains, showing that in the asynchronous regime close to a state of balanced synaptic input from the network, these iterative schemes provide an excellent approximation to the autocorrelation of spike trains in the recurrent network.