Plastic systemic inhibition controls amplitude while allowing phase pattern in a stochastic neural field model

We investigate oscillatory phase pattern formation and amplitude control for a linearized stochastic neuron field model by simulating Mexican-hat-coupled stochastic processes. We find, for several choices of parameters, that spatial pattern formation in the temporal phases of the coupled processes occurs if and only if their amplitudes are allowed to grow unrealistically large. Stimulated by recent work on homeostatic inhibitory plasticity, we introduce static and plastic (adaptive) systemic inhibitory mechanisms to keep the amplitudes stochastically bounded. We find that systems with static inhibition exhibited bounded amplitudes but no sustained phase patterns. With plastic systemic inhibition, on the other hand, the resulting systems exhibit both bounded amplitudes and sustained phase patterns. These results demonstrate that plastic inhibitory mechanisms in neural field models can dynamically control amplitudes while allowing patterns of phase synchronization to develop. Similar mechanisms of plastic systemic inhibition could play a role in regulating oscillatory functioning in the brain.