Abstract
The concept of self-organized criticality (SOC) describes a variety of phenomena ranging from plate tectonics, the dynamics of granular media and stick-slip motion to neural avalanches. In all these cases the dynamics is marginally stable and event sizes obey a characteristic power-law distribution. Criticality was shown to bring about optimal computational capabilities, optimal transmission and storage of information, and sensitivity to sensory stimuli. In neuronal systems the existence of critical avalanches was predicted in a paper of one of the present authors [1] and observed experimentally by Beggs and Plenz [2].
In our previous work, we have shown that an extended critical interval can be obtained in a neural network by incorporation of depressive synapses [3].
In the present study we scrutinize a more realistic dynamics for the synaptic interactions that can be considered as the state-of-the-art in computational modeling of synaptic interaction. Interestingly, the more complex model does not exclude an analytical treatment and it shows a type of stationary state consisting of self-organized critical phase and a subcritical phase that has not been described earlier. The phases are connected by first- or second-order phase transitions in a cusp bifurcation which is implied by the dynamical equations of the underlying biological model [4]. We show that switching between critical and subcritical phase can be induced by synchronized excitatory or inhibitory inputs and study the reliability of switching in dependence of the input strength.We present exact analytical results supported by extensive numerical simulations.
Although presented in the specific context of a neural model, the dynamical structure of our model is of more general interest. It is the first observation of a system that combines a complex classical bifurcation scenario with a robust critical phase. Our study suggests that critical properties of neuronal dynamics in the brain may be considered as a consequence of the regulatory mechanisms at the level of synaptic connections. The system may account not only for SOC behavior, but also for various switching effects observed in the brain. It suggests to explain observations of up and down states in the prefrontal cortex as well as the discrete changes in synaptic potentiation and depression as a network effects. The relation between neural activity and average synaptic strength, which we derived here may account for the reported all-or-none behavior.
