Event-Triggered Stabilisation of Desynchronisation in Networked Oscillatory Systems

What the math gives to ML

The paper provides a constructive mechanism for sparse desynchronisation control: an order-parameter feedback law is interpreted as gradient descent on synchrony, while event-triggered updates preserve stabilisation and guarantee a positive inter-event dwell time. This transfers naturally to recurrent or state-space neural networks whose hidden channels are represented by two-dimensional oscillatory states, where synchronised channel phases can cause representational collapse or loss of dynamical diversity. The direct implementation is to compute a pseudo-phase from each two-dimensional hidden state, apply tangent-space feedback proportional to the gradient of the squared Kuramoto order parameter, and hold that control between event times. The falsifiable prediction is that continuous control produces monotone decay of the synchrony Lyapunov function, whereas event-triggered control retains approximately the same decay with fewer updates and an inter-event time bounded below by the trigger tolerance divided by the maximum control-rate variation.