Controlling complex rhythms: A hierarchical approach to limit cycle switching
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866908490068393984 |
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| author | Saha, Sandip Pal, Suvam Ghosh, Dibakar |
| author_facet | Saha, Sandip Pal, Suvam Ghosh, Dibakar |
| contents | Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering oscillations. The presence of multiple concentric limit cycles reflects distinct behavioral symmetries within a system. In this work, we investigate the hierarchical dynamical transitions from one limit cycle to another, driven by oscillatory excitation while preserving other system properties. We demonstrate that controlling multirhythmicity through hierarchical, stepwise periodic modulation enables reliable switching between rhythmic states. This hierarchical control framework is crucial for applications in neuro-engineering and synthetic biology, where precise, robust modulation of complex rhythmic behaviors enhances system functionality and adaptability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10818 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Controlling complex rhythms: A hierarchical approach to limit cycle switching Saha, Sandip Pal, Suvam Ghosh, Dibakar Adaptation and Self-Organizing Systems Dynamical Systems Limit cycles are self-sustained, closed trajectories in phase space representing (un)-stable, periodic behavior in nonlinear dynamical systems. They underpin diverse natural phenomena, from neuronal firing patterns to engineering oscillations. The presence of multiple concentric limit cycles reflects distinct behavioral symmetries within a system. In this work, we investigate the hierarchical dynamical transitions from one limit cycle to another, driven by oscillatory excitation while preserving other system properties. We demonstrate that controlling multirhythmicity through hierarchical, stepwise periodic modulation enables reliable switching between rhythmic states. This hierarchical control framework is crucial for applications in neuro-engineering and synthetic biology, where precise, robust modulation of complex rhythmic behaviors enhances system functionality and adaptability. |
| title | Controlling complex rhythms: A hierarchical approach to limit cycle switching |
| topic | Adaptation and Self-Organizing Systems Dynamical Systems |
| url | https://arxiv.org/abs/2508.10818 |