Chaotic discretization theorems for forced linear and nonlinear coupled oscillators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911452182347776 |
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| author | Disca, Stefano Coscia, Vincenzo |
| author_facet | Disca, Stefano Coscia, Vincenzo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_10565 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chaotic discretization theorems for forced linear and nonlinear coupled oscillators Disca, Stefano Coscia, Vincenzo Chaotic Dynamics Mathematical Physics Dynamical Systems 39A33 (Primary) 39B12, 37D45, 39A28 (Secondary) 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. |
| title | Chaotic discretization theorems for forced linear and nonlinear coupled oscillators |
| topic | Chaotic Dynamics Mathematical Physics Dynamical Systems 39A33 (Primary) 39B12, 37D45, 39A28 (Secondary) |
| url | https://arxiv.org/abs/2512.10565 |