Self-organized bistability and its possible relevance for brain dynamics

Abstract

Self-organized bistability (SOB) is the counterpart of 'self-organized criticality' (SOC), for systems tuning themselves to the edge of bistability of a discontinuous phase transition, rather than to the critical point of a continuous one. The equations defining the mathematical theory of SOB turn out to bear strong resemblance to a (Landau-Ginzburg) theory recently proposed to analyze the dynamics of the cerebral cortex. This theory describes the neuronal activity of coupled mesoscopic patches of cortex, homeostatically regulated by short-term synaptic plasticity. The theory for cortex dynamics entails, however, some significant differences with respect to SOB, including the lack of a (bulk) conservation law, the absence of a perfect separation of timescales and, the fact that in the former, but not in the second, there is a parameter that controls the overall system state (in blatant contrast with the very idea of self-organization). Here, we scrutinize --by employing a combination of analytical and computational tools-- the analogies and differences between both theories and explore whether in some limit SOB can play an important role to explain the emergence of scale-invariant neuronal avalanches observed empirically in the cortex. We conclude that, actually, in the limit of infinitely slow synaptic-dynamics, the two theories become identical, but the timescales required for the self-organization mechanism to be effective do not seem to be biologically plausible. We discuss the key differences between self-organization mechanisms with/without conservation and with/without infinitely separated timescales. In particular, we introduce the concept of 'self-organized collective oscillations' and scrutinize the implications of our findings in neuroscience, shedding new light into the problems of scale invariance and oscillations in cortical dynamics.

arXiv comment6 figures

References in corpus (23)

• Emergent complex neural dynamics
• Optimal Dynamical Range of Excitable Networks at Criticality
• Dynamical synapses causing self-organized criticality in neural networks
• Colloquium: Criticality and dynamical scaling in living systems
• Criticality in the brain: A synthesis of neurobiology, models and cognition
• Paths to Self-Organized Criticality
• Self-Organized Branching Processes: A Mean-Field Theory for Avalanches
• Avalanches, Barkhausen Noise, and Plain Old Criticality
• Critical brain networks
• Self-Organized Criticality model for Brain Plasticity
• Landau-Ginzburg theory of cortex dynamics: Scale-free avalanches emerge at the edge of synchronization
• Avalanche and spreading exponents in systems with absorbing states
• Tracer Dispersion in a Self-Organized Critical System
• Absorbing-state phase transitions in fixed-energy sandpiles
• Driving, conservation and absorbing states in sandpiles
• Self-organization without conservation: true or just apparent scale-invariance?
• Self-organization without conservation: Are neuronal avalanches generically critical?
• Self-Organized Bistability Associated With First-Order Phase Transitions
• A simple unified view of branching process statistics: random walks in balanced logarithmic potentials
• Short-term synaptic plasticity in the deterministic Tsodyks-Markram model leads to unpredictable network dynamics
• Emergence of slow collective oscillations in neural networks with spike timing dependent plasticity
• Chaos and correlated avalanches in excitatory neural networks with synaptic plasticity
• A microscopic mechanism for self-organized quasi periodicity in random networks of non linear oscillators

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