Global continuation as a complement to traditional continuation and bifurcation analysis

What the math gives to ML

The paper introduces global continuation, which characterizes the responses of practically all coexisting attractors to finite perturbations rather than tracking only locally continued equilibria or periodic orbits. Its transferable asset is basin-level analysis: for each parameter setting, estimate which attractor a perturbed trajectory reaches and use basin fractions as an operational stability and tipping metric. In neural networks this can become a basin-aware robustness monitor and hyperparameter-selection method for recurrent or state-space models, with a quantitative transition signature when the desired attractor's basin fraction collapses.