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 a 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.