Non-normality, reactivity, and intrinsic stochasticity in neural dynamics: a non-equilibrium potential approach
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Muñoz, MA; Burioni, R; Villegas, P; di Santo, Serena. Non-normality, reactivity, and intrinsic stochasticity in neural dynamics: a non-equilibrium potential approach
SponsorshipWe are grateful to the Spanish-MINECO for financial support (under grants FIS2013-43201-P and FIS2017-84256-P; FEDER funds). MAM also acknowledges the support from TeachinParma and the Cariparma foundation.
Intrinsic stochasticity can induce highly non-trivial effects on dynamical systems, such as stochastic resonance, noise induced bistability, and noise-induced oscillations, to name but a few. Here we revisit a mechanism-first investigated in the context of neuroscience-by which relatively small intrinsic (demographic) 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 from (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'. By employing a number of analytical and computational approaches, we further investigate this mechanism and explore the interplay between non-normality and intrinsic stochasticity. In particular, we conclude that the resulting dynamics of 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 the observed values of avalanche exponents.