187 research outputs found
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
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
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
- …