@article{Levnajic2011,
  author    = {Levnajic, Zoran},
  title     = {Emergent multistability and frustration in phase-repulsive networks of oscillators},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {84},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {1},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.84.016231},
  pages     = {10},
  year      = {2011},
  abstract  = {The collective dynamics of oscillator networks with phase-repulsive coupling is studied, considering various network sizes and topologies. The notion of link frustration is introduced to characterize and quantify the network dynamical states. In opposition to widely studied phase-attractive case, the properties of final dynamical states in our model critically depend on the network topology. In particular, each network's total frustration value is intimately related to its topology. Moreover, phase-repulsive networks in general display multiple final frustration states, whose statistical and stability properties are uniquely identifying them.},
  language  = {en}
}
@article{LevnajicPikovskij2011,
  author    = {Levnajic, Zoran and Pikovskij, Arkadij},
  title     = {Network reconstruction from random phase resetting},
  series = {Physical review letters},
  volume    = {107},
  journal   = {Physical review letters},
  number    = {3},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.107.034101},
  pages     = {4},
  year      = {2011},
  abstract  = {We propose a novel method of reconstructing the topology and interaction functions for a general oscillator network. An ensemble of initial phases and the corresponding instantaneous frequencies is constructed by repeating random phase resets of the system dynamics. The desired details of network structure are then revealed by appropriately averaging over the ensemble. The method is applicable for a wide class of networks with arbitrary emergent dynamics, including full synchrony.},
  language  = {en}
}
@article{LevnajicPikovskij2014,
  author    = {Levnajic, Zoran and Pikovskij, Arkadij},
  title     = {Untangling complex dynamical systems via derivative-variable correlations},
  series = {Scientific reports},
  volume    = {4},
  journal   = {Scientific reports},
  publisher = {Nature Publ. Group},
  address   = {London},
  issn      = {2045-2322},
  doi       = {10.1038/srep05030},
  pages     = {6},
  year      = {2014},
  abstract  = {Inferring the internal interaction patterns of a complex dynamical system is a challenging problem. Traditional methods often rely on examining the correlations among the dynamical units. However, in systems such as transcription networks, one unit's variable is also correlated with the rate of change of another unit's variable. Inspired by this, we introduce the concept of derivative-variable correlation, and use it to design a new method of reconstructing complex systems (networks) from dynamical time series. Using a tunable observable as a parameter, the reconstruction of any system with known interaction functions is formulated via a simple matrix equation. We suggest a procedure aimed at optimizing the reconstruction from the time series of length comparable to the characteristic dynamical time scale. Our method also provides a reliable precision estimate. We illustrate the method's implementation via elementary dynamical models, and demonstrate its robustness to both model error and observation error.},
  language  = {en}
}