A simple chaos indicator based on the Lagrangian descriptor difference of neighboring orbits
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909990093062144 |
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| author | Jiménez-López, Javier García-Garrido, Víctor J. |
| author_facet | Jiménez-López, Javier García-Garrido, Víctor J. |
| contents | In this paper we introduce a chaos indicator derivable from Lagrangian descriptors (LDs), defined as the difference in LD values between two neighboring trajectories. This difference LD is remarkably easy to implement and interpret, offering a direct and intuitive measure of dynamical behavior. We provide a heuristic argument linking its growth to the regularity or chaoticity due to the underlying initial condition, considering the arclength-based formulation of LDs. To evaluate its effectiveness, we benchmark it against more elaborate LD-based chaos indicators and the Smaller Aligment Index (SALI) using two prototypical systems: the Hénon-Heiles system and the Chirikov Standard Map. Our results show that, despite its simplicity, the difference LD matches the accuracy of more sophisticated methods, making it a robust and accessible tool for chaos detection in dynamical systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A simple chaos indicator based on the Lagrangian descriptor difference of neighboring orbits Jiménez-López, Javier García-Garrido, Víctor J. Chaotic Dynamics Dynamical Systems In this paper we introduce a chaos indicator derivable from Lagrangian descriptors (LDs), defined as the difference in LD values between two neighboring trajectories. This difference LD is remarkably easy to implement and interpret, offering a direct and intuitive measure of dynamical behavior. We provide a heuristic argument linking its growth to the regularity or chaoticity due to the underlying initial condition, considering the arclength-based formulation of LDs. To evaluate its effectiveness, we benchmark it against more elaborate LD-based chaos indicators and the Smaller Aligment Index (SALI) using two prototypical systems: the Hénon-Heiles system and the Chirikov Standard Map. Our results show that, despite its simplicity, the difference LD matches the accuracy of more sophisticated methods, making it a robust and accessible tool for chaos detection in dynamical systems. |
| title | A simple chaos indicator based on the Lagrangian descriptor difference of neighboring orbits |
| topic | Chaotic Dynamics Dynamical Systems |
| url | https://arxiv.org/abs/2506.16660 |