@misc{ClusellaPolitiRosenblum2016,
  author    = {Clusella, Pau and Politi, Antonio and Rosenblum, Michael},
  title     = {A minimal model of self-consistent partial synchrony},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch Naturwissenschaftliche Reihe},
  number    = {890},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43626},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436266},
  pages     = {19},
  year      = {2016},
  abstract  = {We show that self-consistent partial synchrony in globally coupled oscillatory ensembles is a general phenomenon. We analyze in detail appearance and stability properties of this state in possibly the simplest setup of a biharmonic Kuramoto-Daido phase model as well as demonstrate the effect in limit-cycle relaxational Rayleigh oscillators. Such a regime extends the notion of splay state from a uniform distribution of phases to an oscillating one. Suitable collective observables such as the Kuramoto order parameter allow detecting the presence of an inhomogeneous distribution. The characteristic and most peculiar property of self-consistent partial synchrony is the difference between the frequency of single units and that of the macroscopic field.},
  language  = {en}
}
@misc{PolitiPikovskijUllner2017,
  author    = {Politi, Antonio and Pikovskij, Arkadij and Ullner, Ekkehard},
  title     = {Chaotic macroscopic phases in one-dimensional oscillators},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {721},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-42979},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-429790},
  pages     = {20},
  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}
}