Abstract
The mechanistic understanding of why neuronal population activity hovers on criticality remains unresolved despite the availability of experimental results. Without a coherent mathematical framework, the presence of power-law scaling is not straightforward to reconcile with findings implying epileptiform activity. Although multiple pictures have been proposed to relate the power-law scaling of avalanche statistics to phase transitions, the existence of a phase boundary in parameter space is until now an assumption. Herein, a framework based on differential inclusions, which departs from approaches constructed from differential equations, is shown to offer an adequate consolidation of evidences apparently connected to criticality and those linked to hyperexcitability. Through this framework, the phase boundary is elucidated in a parameter space spanned by variables representing levels of excitation and inhibition in a neuronal network. The interpretation of neuronal populations based on this approach offers insights on the role of pharmacological and endocrinal signaling in the homeostatic regulation of neuronal population activity.