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arXiv · 2509.07487

Statistical properties of homoclinic bursting: an approach using infinite-modal maps toward predicting extreme events

Masaki Nakagawa
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Abstract

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.

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Masaki Nakagawa. 2025-09-09. Statistical properties of homoclinic bursting: an approach using infinite-modal maps toward predicting extreme events. https://doi.org/10.1587/nolta.17.613

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