2025/12/11 by Disca, Stefano, Coscia, Vincenzo
#37D45 #39A28 (Secondary) #39A33 (Primary) 39B12 #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2512.10565
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 ODEs systems describing coupled oscillators subject to an external nonconservative 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 present the bifurcation diagram and perform a bifurcation analysis of the system.