2016/09/30 by Igor V. Ovchinnikov, Wenyuan Li, Yuquan Sun +4
Biochemistry, Genetics and Molecular Biology · Mathematics · Neuroscience · Physics and Astronomy · #Chaos control and synchronization #Chaotic #Context (archaeology) #Criticality #Intermittency #Limit (mathematics) #Lyapunov exponent #Neural dynamics and brain function #Phase (matter) #Stochastic process #Supersymmetry #math.DS #q-bio.NC #stochastic dynamics and bifurcation
paper · pdf · doi:10.3390/sym12050805
published as Symmetry 12, 805 (2020) · elsevier format, updated refs
openalex created_date 2017/05/26 · arxiv created 2020/02/06 · openalex publication_date 2020/05/12 · arxiv updated 2020/05/19 · openalex updated_date 2026/08/05
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.