Chaotic discretization theorems for forced linear and nonlinear coupled oscillators
Abstract
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force, also giving an example of a discrete map that is Li-Yorke chaotic but not topologically transitive. Analytical results are generalized to a modular definition of the problem and to a system of nonlinear oscillators described by polynomial potentials in one coordinate. We perform numerical simulations looking for a strange attractor of the system; furthermore, we perform a bifurcation analysis of the system presenting 1D and 2D bifurcation diagrams, together with spectra of Lyapunov exponents and basins of attraction.
Keywords
Cite
@article{arxiv.2512.10565,
title = {Chaotic discretization theorems for forced linear and nonlinear coupled oscillators},
author = {Stefano Disca and Vincenzo Coscia},
journal= {arXiv preprint arXiv:2512.10565},
year = {2026}
}
Comments
39 pages, 33 figures. This is the author's accepted manuscript (postprint). The final published version is available in Chaos, Solitons & Fractals (Elsevier) under CC BY 4.0, DOI: https://doi.org/10.1016/j.chaos.2026.118086