Homeostatic criticality in neuronal networks

In self-organized criticality (SOC) models, as well in standard phase transitions, is only present for vanishing external fields $h \to 0$. Considering that this rarely the case natural systems, such a restriction poses challenge to explanatory power of these models. Besides that, models dissipative systems like earthquakes, forest fires, and neuronal networks, there no true critical behavior, expressed clean laws obeying finite-size scaling, but scenario called "dirty" or quasi-criticality (SOqC). Here, we propose simple homeostatic mechanisms which promote self-organization coupling strengths, gains, firing thresholds networks. We show with an adequate separation timescales strength threshold dynamics, near (SOqC) can be reached sustained even presence significant input. The adapt cancel inputs ($h$ decreases towards zero). Similar proposed couplings local spin cellular automata, could lead applications earthquake, fire, stellar flare, voting, epidemic modeling.