Discontinuous MSF

Description

This dataset comprises results obtained using three approaches for estimating the Transversal Lyapunov Exponent (TLE) in discontinuous dynamical systems: the two‑probe method, the saltation‑matrix‑based method, and a newly proposed approach based on the estimation of the Jacobian matrix along the oscillator trajectory. The data were generated for two benchmark systems—a piecewise‑linear impact oscillator and a Duffing impact oscillator. In all simulations, the oscillators were assumed to be arranged in spring‑coupled networks. Details of the system equations and parameters are provided in the preprint arXiv:2503.19995. Coupling coefficient ranges: Piecewise‑linear impact oscillator with elastic collision (R = 1.0): σ ∈ [0.0, 3.0] Piecewise‑linear impact oscillator with non‑elastic collision (R = 0.9): σ ∈ [0.0, 3.0] Duffing impact oscillator with elastic collision (R = 1.0): σ ∈ [0.0, 6.0] The results obtained using the two‑oscillator probe are provided in a compressed .zip archive and must be unpacked prior to generating the plots.

Steps to reproduce

Python scripts are shared with the data. Use python 3.x, numpy 1.2.4. scipy 1.9.1 and matplotlib 3.7.5.

Institutions

• Politechnika Lodzka Wydzial Mechaniczny

  Lodz

Categories

Funders

• National Science Centre

  Lesser Poland, Poland

  Grant ID: 2023/49/N/ST8/02436

Licence