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