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| Format: | Recurso digital |
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Zenodo
2026
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| Accès en ligne: | https://doi.org/10.5281/zenodo.18207449 |
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- <p><a href="https://ijetrm.com/issues/files/Jan-2026-10-1768054123-JAN18.pdf" target="_blank" rel="noopener">Phase space descriptions</a> play a major part in the study of complex dynamical systems; but traditional Euclidean<br>formulations do not usually exhibit much of intrinsic periodicity, multi-frequency interactions and topological<br>constraints found in real-world systems. We propose a new analytical structure of the torus-based phase space<br>representations in this work, which is aimed at offering a mathematically consistent and topologically faithful<br>description of the systems with cyclic and quasi-periodic dynamics. The suggested construction takes the form of<br>formalization of the production of low-dimensional toroidal manifolds directly out of the variables of the system,<br>allowing the retention of periodicity conditions of the boundaries and invariant structures that are being deformed<br>under the standard representations. The framework has analytical properties, such as stability features and invariant<br>sets, which are obtained and analyzed. We use a set of numerical experiments with a set of representative nonlinear<br>dynamical systems, where the results of the computations are the toroidal orbits as compared to the Euclidean<br>counterparts. The results of the simulations prove that the proposed approach provides better structural coherence,<br>better interpretability of the system dynamics, and better resistance to changes in parameters and noise. These results<br>demonstrate the benefits of representations using torus when it comes to analytical understanding as well as towards<br>computational modeling. The framework has a generalizable structure that can be applied to a large variety of complex<br>systems, providing a single methodology of how to combine topology-aware analysis with validation through<br>simulations.</p>