Extreme Events in the Higgs Oscillator: A Dynamical Study and Forecasting Approach

TL;DR

This paper investigates the complex dynamics of the Higgs oscillator, identifies conditions leading to extreme events, and employs neural networks to forecast these rare but significant occurrences.

Contribution

It provides a detailed dynamical analysis of the Higgs oscillator with damping and forcing, and introduces a neural network-based approach for predicting extreme events.

Findings

Bifurcation phenomena such as symmetry breaking and period doubling are observed.

Extreme events occur due to interior crises in the system.

LSTM neural networks can effectively forecast extreme events.

Abstract

Many dynamical systems exhibit unexpected large amplitude excursions in the chronological progression of a state variable. In the present work, we consider the dynamics associated with the one-dimensional Higgs oscillator which is realized through gnomic projection of a harmonic oscillator defined on a spherical space of constant curvature onto a Euclidean plane which is tangent to the spherical space. While studying the dynamics of such a Higgs oscillator subjected to damping and an external forcing, various bifurcation phenomena, such as symmetry breaking, period doubling, and intermittency crises are encountered. As the driven parameter increases, the route to chaos takes place via intermittency crisis and we also identify the occurrence of extreme events due to the interior crisis. The study of probability distribution also confirms the occurrence of extreme events. Finally, we train the Long Short-Term Memory neural network model with the time-series data to forecast the extreme events (EEs).