Collective dynamics in the presence of finite-width pulses.

Afifurrahman Afifurrahman,Ekkehard Ullner,Antonio Politi

doi:10.1063/5.0046691

Afifurrahman Afifurrahman, Ekkehard Ullner + Show 1 more

Open Access

https://doi.org/10.1063/5.0046691

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Abstract

The idealization of neuronal pulses as δ-spikes is a convenient approach in neuroscience but can sometimes lead to erroneous conclusions. We investigate the effect of a finite pulse width on the dynamics of balanced neuronal networks. In particular, we study two populations of identical excitatory and inhibitory neurons in a random network of phase oscillators coupled through exponential pulses with different widths. We consider three coupling functions inspired by leaky integrate-and-fire neurons with delay and type I phase-response curves. By exploring the role of the pulse widths for different coupling strengths, we find a robust collective irregular dynamics, which collapses onto a fully synchronous regime if the inhibitory pulses are sufficiently wider than the excitatory ones. The transition to synchrony is accompanied by hysteretic phenomena (i.e., the co-existence of collective irregular and synchronous dynamics). Our numerical results are supported by a detailed scaling and stability analysis of the fully synchronous solution. A conjectured first-order phase transition emerging for δ-spikes is smoothed out for finite-width pulses.

Highlights

Irregular firing activity is a robust phenomenon observed in certain areas of mammalian brain, such as hippocampus or cortical neurons1,2
This paper focuses on a regime called collective irregular dynamics (CID), which arises in networks of oscillators
All indicators reveal the existence of two distinct phases: a synchronous regime arising for small β values, and CID observed beyond a critical point which depends on the network size: the transition is discontinuous

Summary

INTRODUCTION

Irregular firing activity is a robust phenomenon observed in certain areas of mammalian brain, such as hippocampus or cortical neurons. There are (at least) two mechanisms leading to CID: (i) the intrinsic infinite dimensionality of the nonlinear equations describing whole populations of oscillators; (ii) an imperfect balance between excitatory and inhibitory activity Within the former framework, no truly complex collective dynamics can arise in mean-field models of identical oscillators of Kuramoto type. It is sufficient to consider either ensembles of heterogeneous oscillators: e.g., leaky integrate-and-fire (LIF) neurons, and pulse-coupled phase oscillators (notice that in these cases, Ott-Antonsen Ansatz does not apply) Within the latter framework, an irregular activity was first observed and described in networks of binary units, as a consequence of a (statistical) balance between excitation and inhibition. Our first result is that CID is observed in the presence of finite pulse-width, we find a transition to full synchrony when the inhibitory pulses are sufficiently longer than excitatory ones. Here we report several power spectra to testify the stochastic-like dynamics of macroscopic (average) observables

DELTA PULSE

IDENTICAL FINITE-WIDTH PULSES

FULL SETUP

Robustness

CONCLUSION AND OPEN PROBLEMS