Control of Inhibition-Stabilized Oscillations in Wilson-Cowan Networks with Homeostatic Plasticity

Interactions between excitatory and inhibitory neurons in the cerebral cortex give rise to different regimes of activity and modulate brain oscillations. A prominent regime in the cortex is the inhibition-stabilized network (ISN), defined by strong recurrent excitation balanced by inhibition. While theoretical models have captured the response of brain circuits in the ISN state, their connectivity is typically hard-wired, leaving unanswered how a network may self-organize to an ISN state and dynamically switch between ISN and non-ISN states to modulate oscillations. Here, we introduce a mean-rate model of coupled Wilson-Cowan equations, link ISN and non-ISN states to Kolmogorov-Sinai entropy, and demonstrate how homeostatic plasticity (HP) allows the network to express both states depending on its level of tonic activity. This mechanism enables the model to capture a broad range of experimental effects, including (i) a paradoxical decrease in inhibitory activity, (ii) a phase offset between excitation and inhibition, and (iii) damped gamma oscillations. Further, the model accounts for experimental work on asynchronous quenching, where an external input suppresses intrinsic oscillations. Together, findings show that oscillatory activity is modulated by the dynamical regime of the network under the control of HP, thus advancing a framework that bridges neural dynamics, entropy, oscillations, and synaptic plasticity.