Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.07487 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911568100327424 |
|---|---|
| author | Nakagawa, Masaki |
| author_facet | Nakagawa, Masaki |
| contents | Predicting extreme events in nonlinear dynamical systems is challenging due to a limited understanding of their statistical properties. This study numerically and theoretically investigates the statistical properties of infinite-modal maps arising from homoclinic bursting to predict extreme events. The numerical investigation presents bifurcation diagrams, Lyapunov exponents, height probability distributions, and interevent interval probability distributions for infinite-modal maps. The theoretical analysis derives analytical formulae for these statistical properties using a randomization theory of infinite-modal maps. Furthermore, a parameter estimation method for infinite-modal maps is proposed, utilizing the derived analytical formula, which enables practical application of the theoretical results. Finally, the study demonstrates the applicability of the approach in analyzing non-stationary data with time-dependent parameters. These findings provide a foundation for the prediction of extreme events based on their mechanism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07487 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Statistical properties of homoclinic bursting: an approach using infinite-modal maps toward predicting extreme events Nakagawa, Masaki Chaotic Dynamics Predicting extreme events in nonlinear dynamical systems is challenging due to a limited understanding of their statistical properties. This study numerically and theoretically investigates the statistical properties of infinite-modal maps arising from homoclinic bursting to predict extreme events. The numerical investigation presents bifurcation diagrams, Lyapunov exponents, height probability distributions, and interevent interval probability distributions for infinite-modal maps. The theoretical analysis derives analytical formulae for these statistical properties using a randomization theory of infinite-modal maps. Furthermore, a parameter estimation method for infinite-modal maps is proposed, utilizing the derived analytical formula, which enables practical application of the theoretical results. Finally, the study demonstrates the applicability of the approach in analyzing non-stationary data with time-dependent parameters. These findings provide a foundation for the prediction of extreme events based on their mechanism. |
| title | Statistical properties of homoclinic bursting: an approach using infinite-modal maps toward predicting extreme events |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2509.07487 |