Nonreciprocal amplification toward chaos in a chain of Duffing oscillators

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.