Abstract
In many stochastic dynamical systems, ordinary chaotic behavior is preceded by a full-dimensional phase that exhibits 1/f-type power spectra and/or scale-free statistics of (anti)instantons such as neuroavalanches, earthquakes, etc. In contrast with the phenomenological concept of self-organized criticality, the recently found approximation-free supersymmetric theory of stochastics (STS) identifies this phase as the noise-induced chaos (N-phase), i.e., the phase where the topological supersymmetry pertaining to all stochastic dynamical systems is broken spontaneously by the condensation of the noise-induced (anti)instantons. Here, we support this picture in the context of neurodynamics. We study a 1D chain of neuron-like elements and find that the dynamics in the N-phase is indeed featured by positive stochastic Lyapunov exponents and dominated by (anti)instantonic processes of (creation) annihilation of kinks and antikinks, which can be viewed as predecessors of boundaries of neuroavalanches. We also construct the phase diagram of emulated stochastic neurodynamics on Spikey neuromorphic hardware and demonstrate that the width of the N-phase vanishes in the deterministic limit in accordance with STS. As a first result of the application of STS to neurodynamics comes the conclusion that a conscious brain can reside only in the N-phase.
Highlights
IntroductionIt is well established that many stochastic dynamical systems close to the “edge of chaos”
At non-zero noises, ordinary chaos is preceded by a noise-induced chaotic phase where the topological supersymmetry is broken by the condensation of noise-inducedinstantonic configurations
We supported this picture by numerical studies of a 1D chain of neuron-like elements and experimental emulation of stochastic neurodynamics using neuromorphic hardware
Summary
It is well established that many stochastic dynamical systems close to the “edge of chaos”. After 25 years of the history of SOC, it is still unclear what SOC is exactly from a theoretical point of view (see [15] for a review on various interpretations of SOC) and whether ND in a healthy brain can be characterized as SOC (see, e.g., [25,26,27,28,29] and the references therein) It was understood [30,31] that a more rigorous theoretical picture of DC could be based on the Goldstone theorem stating that a spontaneous breakdown of a global continuous symmetry must lead to the long-range behavior in full-dimensional phases.
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