@article{LepriPikovskij2014,
  author    = {Lepri, Stefano and Pikovskij, Arkadij},
  title     = {Nonreciprocal wave scattering on nonlinear string-coupled oscillators},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {24},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {4},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.4899205},
  pages     = {9},
  year      = {2014},
  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 analyzed 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. (C) 2014 AIP Publishing LLC.},
  language  = {en}
}
@article{LepriPikovsky2022,
  author    = {Lepri, Stefano and Pikovsky, Arkady},
  title     = {Phase-locking dynamics of heterogeneous oscillator arrays},
  series = {Chaos, solitons \& fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science},
  volume    = {155},
  journal   = {Chaos, solitons \& fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0960-0779},
  doi       = {10.1016/j.chaos.2021.111721},
  pages     = {8},
  year      = {2022},
  abstract  = {We consider an array of nearest-neighbor coupled nonlinear autonomous oscillators with quenched ran-dom frequencies and purely conservative coupling. We show that global phase-locked states emerge in finite lattices and study numerically their destruction. Upon change of model parameters, such states are found to become unstable with the generation of localized periodic and chaotic oscillations. For weak nonlinear frequency dispersion, metastability occur akin to the case of almost-conservative systems. We also compare the results with the phase-approximation in which the amplitude dynamics is adiabatically eliminated.},
  language  = {en}
}