Activated switching between coexisting limit cycles

What the math gives to ML

The paper demonstrates noise-activated switching between coexisting limit cycles, showing that the relevant activation barrier is not a static potential difference but the Freidlin-Wentzell action of the most probable transition path. Switching rates obey an Arrhenius-like law, with log switching rate approximately linear in inverse noise intensity and slope determined by the minimum action between periodic attractors. A transferable neural-network mechanism is an RNN or state-space model with structured coexisting latent cycles and calibrated noise-driven hopping, enabling multimodal long-horizon prediction while replacing uncontrolled mode collapse with an action-controlled transition process.