Nonreciprocal amplification toward chaos in a chain of Duffing oscillators

TL;DR

This paper explores how nonreciprocal coupling in a chain of nonlinear Duffing oscillators leads to complex bifurcations, chaos, and unique amplitude behaviors, extending the concept of non-Hermitian skin effect to nonlinear dynamics.

Contribution

It introduces a nonlinear extension of nonreciprocal amplification using Duffing oscillators, revealing new bifurcation phenomena and chaotic regimes.

Findings

Bifurcations from limit cycles to chaos and hyper-chaos occur with added units.

Chaotic regimes show amplitude saturation with decreasing amplitudes per unit.

Unidirectional coupling decomposes attractors into phase space subspaces.

Abstract

A chain of harmonic oscillators with nonreciprocal coupling exhibits characteristic amplification behavior that serves as a classical analog of the non-Hermitian skin effect (NHSE). We extend this concept of nonreciprocal amplification to nonlinear dynamics by employing double-well Duffing oscillators arranged in ring-structured units. The addition of units induces bifurcations of attractors, driving transitions from limit cycles to tori, chaos, and hyper-chaos. Unidirectional couplings between units enable the decomposition of attractors in phase space into projected subspaces corresponding to each unit. In the chaotic regime, amplitude saturation emerges, characterized by monotonically decreasing amplitudes within a unit -- in sharp contrast to} the increasing profiles seen in the linear NHSE. This work uncovers novel bifurcation behavior resulting from the intricate interplay between nonreciprocity and nonlinearity.