Nonreciprocal wave scattering on nonlinear string-coupled oscillators

TL;DR

This paper investigates how nonlinear oscillators attached to a string cause nonreciprocal wave scattering, leading to potential applications like nonreciprocal modulators and chaotic diodes, through analytical and numerical methods.

Contribution

It introduces a model of wave scattering on nonlinear string-coupled oscillators, revealing nonreciprocal transmission and complex dynamics such as chaos and bifurcations.

Findings

Nonreciprocal wave transmission due to oscillator nonlinearity.

Identification of regimes with quasiperiodic and chaotic scattering.

Discovery of a 'chaotic diode' regime with asymmetric transmission behavior.

Abstract

We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: the same wave is transmitted differently in two directions. Periodic regimes of scattering are analysed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a "chaotic diode", where transmission is periodic in one direction and chaotic in the opposite one, is reported.