  In large-scale neural networks, coherent limit cycle oscillations usually
coexist with unstable incoherent equilibrium states, which are not observed
experimentally. We implement a first-order dynamic controller to stabilize
unknown equilibrium states and suppress coherent oscillations. The
stabilization of incoherent equilibria associated with unstable focus and
saddle is considered. The algorithm is demonstrated for networks composed of
quadratic integrate-and-fire (QIF) neurons and Hindmarsh-Rose neurons. The
microscopic equations of an infinitely large QIF neural network can be reduced
to an exact low-dimensional system of mean-field equations, which makes it
possible to study the control problem analytically.
