Nonreciprocal wave scattering on nonlinear string-coupled oscillators

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.

Version accepted for publication

References in corpus (6)

• Unidirectional Nonlinear PT-symmetric Optical Structures
• Bistable diode action in left-handed periodic structures
• Spontaneous symmetry breaking in a nonlinear double-well structure
• Nonreciprocal switching thresholds in coupled nonlinear microcavities
• Wave-packet rectification in nonlinear electronic systems: A tunable Aharonov-Bohm diode
• Localized modes in two-dimensional Schroedinger lattices with a pair of nonlinear sites