Desynchronization of large-scale neural networks by stabilizing unknown unstable incoherent equilibrium states

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.