| _version_ | 1866902093717045248 |
|---|---|
| author | Dr Reji Kurien Thomas |
| author_facet | Dr Reji Kurien Thomas |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18207449 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | TORUS-BASED PHASE SPACE REPRESENTATIONS FOR COMPLEX ENVIRONMENTAL SYSTEMS. Dr Reji Kurien Thomas Toroidal phase space; nonlinear dynamical systems; topological representations; novel analytical framework; numerical simulation; complex systems <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> |
| title | TORUS-BASED PHASE SPACE REPRESENTATIONS FOR COMPLEX ENVIRONMENTAL SYSTEMS. |
| topic | Toroidal phase space; nonlinear dynamical systems; topological representations; novel analytical framework; numerical simulation; complex systems |
| url | https://doi.org/10.5281/zenodo.18207449 |