Estimating Unstable Limit Cycles from Small Perturbations: A Minimal-Data-Driven Approach

Unstable solutions, though less prominent than stable ones, are essential in assessing the dynamical integrity of stable steady-states, as basin boundaries are often formed by unstable saddle-type solutions and their stable manifolds. This study introduces a data-driven method to estimate unstable limit cycles around stable equilibria using only small perturbation trajectories near the equilibrium. The approach requires no mathematical model, relying solely on a single phase-space trajectory, making it computationally efficient and practical for real-world applications.