Chaotic discretization theorems for forced linear and nonlinear coupled oscillators

Stefano Disca and Vincenzo Coscia

Chaos, Solitons & Fractals, 2026, vol. 208, issue P1

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: Coupled oscillators; Li–Yorke chaos; Topological transitivity; Strange attractor; Bifurcation analysis (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:208:y:2026:i:p1:s0960077926002274

DOI: 10.1016/j.chaos.2026.118086

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