@article{DeFreitasVianaGrebogi2004,
  author    = {De Freitas, M. S. T. and Viana, R. L. and Grebogi, Celso},
  title     = {Basins of attraction of periodic oscillations in suspension bridges},
  issn      = {0924-090X},
  year      = {2004},
  abstract  = {We consider the dynamics of the lowest order transversal vibration mode of a suspension bridge, for which the hangers are treated as one-sided springs, according to the model of Lazer and McKeena [SIAM Review 58, 1990, 537]. We analyze in particular the multi-stability of periodic attractors and the basin of attraction structure in phase space and its dependence with the model parameters. The parameter values used in numerical simulations have been estimated from a number of bridges built in the United States and in the United Kingdom, thus taking into account realistic, yet sometimes simplified, structural, aerodynamical, and physical considerations},
  language  = {en}
}
@article{FreitasMacauPikovskij2015,
  author    = {Freitas, Celso and Macau, Elbert and Pikovskij, Arkadij},
  title     = {Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {25},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {4},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.4919246},
  pages     = {8},
  year      = {2015},
  abstract  = {We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones. (C) 2015 AIP Publishing LLC.},
  language  = {en}
}