Synchronization and Control in Bistable Oscillator Networks: Towards Epilepsy Regulation

This paper studies networks of diffusively-coupled bistable oscillators. This class of oscillators has been shown before to be suitable for capturing epileptic dynamics, since its stable equilibrium can describe normal neural activity, while its stable limit cycle signifies seizure events. To investigate seizure propagation in brain networks, a sufficient condition to ensure synchronization of the set of oscillators is established. The synchronized network inherits the property of bistability from the single oscillators, i.e., the network can transition between a stable equilibrium and a limit cycle manifold, capturing network-level onsets and offsets of generalized seizures. To prevent the network from converging towards the limit cycle, a controller that targets a subset of the oscillators is proposed, which is proven to globally stabilize the equilibrium. Numerical studies are conducted to validate the theoretical findings.