187 research outputs found

    Nonreciprocal wave scattering on nonlinear string-coupled oscillators

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    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.Comment: Version accepted for publicatio

    Stochastic bursting in unidirectionally delay-coupled noisy excitable systems

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    We show that \emph{stochastic bursting} is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation, i.e., when the time delays in each connection are much larger than the characteristic duration of the spikes, the observed rather coherent spike pattern can be described by idealized coupled point processes with a leader-follower relationship. We derive analytically the statistics of the spikes in each unit, pairwise correlations between any two units, and the spectrum of the total output from the network. Theory is in a good agreement with the simulations with a network of theta-neurons.Comment: accepted in Chao
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