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arXiv · 2512.10565

Chaotic discretization theorems for forced linear and nonlinear coupled oscillators

Stefano Disca·Vincenzo Coscia
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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.

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Stefano Disca, Vincenzo Coscia. 2025-12-11. Chaotic discretization theorems for forced linear and nonlinear coupled oscillators. https://doi.org/10.1016/j.chaos.2026.118086

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