Extreme events in the Higgs oscillator: A dynamical study and forecasting approach

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Theoretical Physics
• Computational Neuroscience

Background:

• Dynamical systems can exhibit unpredictable large-amplitude excursions.
• The Higgs oscillator, derived from a spherical harmonic oscillator, presents complex dynamics when projected onto a Euclidean plane.
• Understanding these dynamics is crucial for various scientific fields.

Purpose of the Study:

• To investigate the bifurcation phenomena and route to chaos in a damped, driven one-dimensional Higgs oscillator.
• To identify and characterize extreme events arising from intermittency and interior crises.
• To develop a predictive model for extreme events using machine learning.

Main Methods:

• Analysis of the Higgs oscillator dynamics under damping and external forcing.
• Identification of bifurcations including symmetry breaking, period doubling, and intermittency crises.
• Application of probability distribution analysis to confirm extreme events.
• Training a long short-term memory (LSTM) neural network on time-series data for event forecasting.

Main Results:

• The Higgs oscillator exhibits a route to chaos via intermittency crisis as the driven parameter increases.
• Extreme events are identified and confirmed through interior crisis and probability distribution studies.
• The LSTM model demonstrates capability in forecasting these extreme events.

Conclusions:

• The Higgs oscillator is a valuable model for studying chaos and extreme events in nonlinear systems.
• Intermittency and interior crises are key mechanisms leading to extreme events.
• LSTM networks offer a promising approach for predicting extreme events in complex dynamical systems.