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arXiv · 1407.6555

Nonreciprocal wave scattering on nonlinear string-coupled oscillators

Stefano Lepri·Arkady Pikovsky
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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.

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Stefano Lepri, Arkady Pikovsky. 2014-10-29. Nonreciprocal wave scattering on nonlinear string-coupled oscillators. https://doi.org/10.1063/1.4899205

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