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.
Fields of Study & Subjects
Chaos control and synchronization
Quantum chaos and dynamical systems
Control and Stability of Dynamical Systems
Publication details
- Journal / source
- Chaos Solitons & Fractals
- Publisher
- Elsevier BV
- Volume
- 208
- Pages
- 118086–118086
- Publication date
- 17 February 2026
- Language
- EN