Mechanisms for extreme events in position-dependent mass systems

Abstract

Oscillators defined on curved spaces provide a natural framework for exploring geometry-induced nonlinear dynamics. The two-dimensional Mathews-Lakshmanan oscillator and Higgs oscillator are prominent examples of geometrically induced nonlinear oscillators. The two-dimensional Higgs oscillator in flat space arises from a conformal (stereographic) projection of the harmonic oscillator on the sphere S2 onto the two-dimensional plane. Its one-dimensional counterpart, defined by a non-Euclidean geometry with curvature parameter, exhibits chaotic dynamics and extreme events (EEs) when subjected to damping and external driving forces [1]. In this work, we introduce coupling through mass interaction among multiple one-dimensional damped and forced Higgs oscillators and investigate the resulting collective nonlinear dynamics within a many-particle framework. More importantly, we establish the connection between the conformal mass m(x) and the extrema of velocity through a power-law relation, demonstrating how the conformal mass regulates the turning points leading to the emergence of extreme events (EEs). Furthermore, to provide additional insight into the underlying mechanism, we quantify the energy synchronization error among the oscillators, thereby revealing how energy synchronization evolves during the onset of EEs.