Electronic Bursting Neuron: design, equations and hardware implementation

What the math gives to ML

The paper gives a compact third-order phase-locked-loop dynamical system whose state variables naturally produce oscillations, bursts, and quiescent intervals, while remaining simple enough for analog implementation. Its transferable asset is a hardware-friendly recurrent cell with explicit timescale separation through \(\varepsilon_1\) and \(\varepsilon_2\), nonlinear phase feedback through \(\cos(\phi)\), and an internal hierarchy of fast and slow states. A practical ML test is to replace selected LIF or gated-RNN units with this differentiable bursting cell and train it with a surrogate spike function, measuring whether burst timing improves temporal classification or reduces the number of recurrent units needed.