@article{PolitiPikovskijUllner2017,
  author    = {Politi, Antonio and Pikovskij, Arkadij and Ullner, Ekkehard},
  title     = {Chaotic macroscopic phases in one-dimensional oscillators},
  series = {European physical journal special topics},
  volume    = {226},
  journal   = {European physical journal special topics},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2017-70056-4},
  pages     = {1791 -- 1810},
  year      = {2017},
  abstract  = {The connection between the macroscopic description of collective chaos and the underlying microscopic dynamics is thoroughly analysed in mean-field models of one-dimensional oscillators. We investigate to what extent infinitesimal perturbations of the microscopic configurations can provide information also on the stability of the corresponding macroscopic phase. In ensembles of identical one-dimensional dynamical units, it is possible to represent the microscopic configurations so as to make transparent their connection with the macroscopic world. As a result, we find evidence of an intermediate, mesoscopic, range of distances, over which the instability is neither controlled by the microscopic equations nor by the macroscopic ones. We examine a whole series of indicators, ranging from the usual microscopic Lyapunov exponents, to the collective ones, including finite-amplitude exponents. A system of pulse-coupled oscillators is also briefly reviewed as an example of non-identical phase oscillators where collective chaos spontaneously emerges.},
  language  = {en}
}
@article{RaabUllnerMenzel2000,
  author    = {Raab, Volker and Ullner, Ekkehard and Menzel, Ralf},
  title     = {Novel External Resonators for High Power Diode Lasers with Improved Beam Quality},
  year      = {2000},
  language  = {en}
}
@article{VolkovUllnerZaikinetal.2003,
  author    = {Volkov, E. I. and Ullner, Ekkehard and Zaikin, Alexei A. and Kurths, J{\"u}rgen},
  title     = {Frequency-dependent stochastic resonance in inhibitory coupled excitable systems},
  issn      = {1063-651X},
  year      = {2003},
  abstract  = {We study frequency selectivity in noise-induced subthreshold signal processing in a system with many noise- supported stochastic attractors which are created due to slow variable diffusion between identical excitable elements. Such a coupling provides coexisting of several average periods distinct from that of an isolated oscillator and several phase relations between elements. We show that the response of the coupled elements under different noise levels can be significantly enhanced or reduced by forcing some elements in resonance with these new frequencies which correspond to appropriate phase relations},
  language  = {en}
}
@article{VolkovUllnerKurths2005,
  author    = {Volkov, E. I. and Ullner, Ekkehard and Kurths, J{\"u}rgen},
  title     = {Stochastic multiresonance in the coupled relaxation oscillators},
  issn      = {1054-1500},
  year      = {2005},
  abstract  = {We study the noise-dependent dynamics in a chain of four very stiff excitable oscillators of the FitzHugh- Nagumo type locally coupled by inhibitor diffusion. We could demonstrate frequency- and noise-selective signal acceptance which is based on several noise-supported stochastic attractors that arise owing to slow variable diffusion between identical excitable elements. The attractors have different average periods distinct from that of an isolated oscillator and various phase relations between the elements. We explain the correspondence between the noise-supported stochastic attractors and the observed resonance peaks in the curves for the linear response versus signal frequency. (C) 2005 American Institute of Physics},
  language  = {en}
}