The Dynamics of Balanced Spiking Neuronal Networks Under Poisson Drive Is Not Chaotic.

Qing-Long L Gu,Douglas Zhou,Gregor Kovačič,Zhong-Qi K Tian,David Cai

doi:10.3389/fncom.2018.00047

Abstract

Some previous studies have shown that chaotic dynamics in the balanced state, i.e., one with balanced excitatory and inhibitory inputs into cortical neurons, is the underlying mechanism for the irregularity of neural activity. In this work, we focus on networks of current-based integrate-and-fire neurons with delta-pulse coupling. While we show that the balanced state robustly persists in this system within a broad range of parameters, we mathematically prove that the largest Lyapunov exponent of this type of neuronal networks is negative. Therefore, the irregular firing activity can exist in the system without the chaotic dynamics. That is the irregularity of balanced neuronal networks need not arise from chaos.

Highlights

Neural spiking activity in the brain is highly irregular (Britten et al, 1993; Shadlen and Newsome, 1998; Compte et al, 2003; London et al, 2010)
Existence of Balanced States In Vreeswijk and Sompolinsky (1998), the properties of the balanced state are shown in detail with binary neuronal networks
We use numerical simulations to investigate whether the current-based I&F neuronal network coupled with deltapulse interactions can exhibit the dynamical characteristics of a balanced state

Summary

Introduction

Neural spiking activity in the brain is highly irregular (Britten et al, 1993; Shadlen and Newsome, 1998; Compte et al, 2003; London et al, 2010). It is believed that the irregularity of the spiking activity can reflect an underlying rich coding structure for information processing (Hertz and Prügel-Bennett, 1996; Gütig and Sompolinsky, 2006; Sussillo and Abbott, 2009; Monteforte and Wolf, 2012). This viewpoint naturally leads to the investigation of the origin of the irregular neuronal activity. It has been found that, in vivo studies, the balanced excitation and inhibition in ferrets’ prefrontal cortex can substantially influence the neuronal activity (Haider et al, 2006)

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Conclusion