Empirical Tests of Persistence Collapse across Multiple Dynamical Systems

This work presents an extended empirical investigation of persistence behavior in nonlinear dynamical systems. The study builds on earlier experiments (V1 and V2) that introduced an empirical framework for measuring persistence collapse under perturbation. The present version (V3) extends the experimental program by introducing cross-system validation across three structurally distinct dynamical systems: the standard map, the Hénon map, and the logistic map. These systems represent different dynamical classes, including Hamiltonian chaos, dissipative strange attractors, and one-dimensional chaotic maps. For each system, trajectories are simulated across parameter sweeps covering the onset and development of chaotic behavior. Persistence is measured using a first-exit criterion within an admissibility corridor defined by a constraint bound. Trajectories are considered to fail when they leave the admissible region. The experiment therefore measures persistence survival without applying corrective projection, allowing direct observation of collapse behavior in the underlying dynamics. Multiple perturbation operators are applied to test robustness of the persistence transition. These include stochastic noise perturbations as well as discontinuous and alternative update operators. Survival probabilities are computed across trajectory ensembles and parameter ranges, producing persistence curves that characterize stability regions and collapse transitions. Across all tested systems, the survival curves exhibit a common structural pattern consisting of a high-survival plateau, a transition region of weakening persistence, and a sharp collapse. Perturbations shift the collapse location but do not remove the overall transition structure. These results suggest that the observed persistence collapse behavior is not specific to a single dynamical system. This work extends the empirical tests introduced in V1 and V2 by incorporating multiple dynamical systems and expanded perturbation analysis. The experiments provide additional evidence that persistence collapse may reflect a broader structural property of chaotic dynamics, motivating further investigation in additional systems and higher-resolution parameter studies. All experiment code, configuration files, figures, and summary datasets used to generate the results are included to support reproducibility.