@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}
}
@article{ClusellaPolitiRosenblum2016,
  author    = {Clusella, Pau and Politi, Antonio and Rosenblum, Michael},
  title     = {A minimal model of self-consistent partial synchrony},
  series = {NEW JOURNAL OF PHYSICS},
  volume    = {18},
  journal   = {NEW JOURNAL OF PHYSICS},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/18/9/093037},
  pages     = {15},
  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}
}
@book{PikovskijPoliti2016,
  author    = {Pikovskij, Arkadij and Politi, Antonio},
  title     = {Lyapunov Exponents},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  isbn      = {978-1-107-03042-8},
  publisher      = {Universit{\"a}t Potsdam},
  pages     = {XII, 285},
  year      = {2016},
  abstract  = {Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers.},
  language  = {en}
}