Non-normality, reactivity, and intrinsic stochasticity in neural dynamics: a non-equilibrium potential approach

TL;DR

This paper investigates how intrinsic stochasticity and non-normality in neural systems lead to complex, non-equilibrium dynamics such as avalanching behavior, emphasizing the role of curl flux and introducing the concept of non-linear reactivity.

Contribution

It introduces a non-equilibrium potential framework to analyze the interplay of non-normality and stochasticity in neural dynamics, highlighting the importance of curl flux and non-linear reactivity.

Findings

Intrinsic stochasticity can induce avalanching in systems with a stable fixed point.

Non-normality leads to reactive dynamics and non-equilibrium behavior.

A non-equilibrium potential approach reveals the role of curl flux in these systems.

Abstract

Intrinsic stochasticity can induce highly non-trivial effects on dynamical systems, including stochastic and coherence resonance, noise induced bistability, noise-induced oscillations, to name but a few. In this paper we revisit a mechanism first investigated in the context of neuroscience by which relatively small demographic (intrinsic) fluctuations can lead to the emergence of avalanching behavior in systems that are deterministically characterized by a single stable fixed point (up state). The anomalously large response of such systems to stochasticity stems (or is strongly associated with) the existence of a "non-normal" stability matrix at the deterministic fixed point, which may induce the system to be "reactive". Here, we further investigate this mechanism by exploring the interplay between non-normality and intrinsic (demographic) stochasticity, by employing a number of analytical and computational approaches. We establish, in particular, that the resulting dynamics in this type of systems cannot be simply derived from a scalar potential but, additionally, one needs to consider a curl flux which describes the essential non-equilibrium nature of this type of noisy non-normal systems. Moreover, we shed further light on the origin of the phenomenon, introduce the novel concept of "non-linear reactivity", and rationalize of the observed the value of the emerging avalanche exponents.