@article{NagornovOsipoyKomarovetal.2016,
  author    = {Nagornov, Roman and Osipoy, Grigory and Komarov, Maxim and Pikovskij, Arkadij and Shilnikov, Andrey},
  title     = {Mixed-mode synchronization between two inhibitory neurons with post-inhibitory rebound},
  series = {Communications in nonlinear science \& numerical simulation},
  volume    = {36},
  journal   = {Communications in nonlinear science \& numerical simulation},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {1007-5704},
  doi       = {10.1016/j.cnsns.2015.11.024},
  pages     = {175 -- 191},
  year      = {2016},
  abstract  = {We study an array of activity rhythms generated by a half-center oscillator (HCO), represented by a pair of reciprocally coupled neurons with post-inhibitory rebounds (PIR). Such coupling induced bursting possesses two time scales, one for fast spiking and another for slow quiescent periods, is shown to exhibit an array of synchronization properties. We discuss several HCO configurations constituted by two endogenous bursters, by tonic-spiking and quiescent neurons, as well as mixed-mode configurations composed of neurons of different type. We demonstrate that burst synchronization can be accompanied by complex, often chaotic, interactions of fast spikes within synchronized bursts. (C) 2015 Elsevier B.V. All rights reserved.},
  language  = {en}
}
@article{KomarovPikovskij2014,
  author    = {Komarov, Maxim and Pikovskij, Arkadij},
  title     = {The Kuramoto model of coupled oscillators with a bi-harmonic coupling function},
  series = {Physica : D, Nonlinear phenomena},
  volume    = {289},
  journal   = {Physica : D, Nonlinear phenomena},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0167-2789},
  doi       = {10.1016/j.physd.2014.09.002},
  pages     = {18 -- 31},
  year      = {2014},
  abstract  = {We study synchronization in a Kuramoto model of globally coupled phase oscillators with a bi-harmonic coupling function, in the thermodynamic limit of large populations. We develop a method for an analytic solution of self-consistent equations describing uniformly rotating complex order parameters, both for single-branch (one possible state of locked oscillators) and multi-branch (two possible values of locked phases) entrainment. We show that synchronous states coexist with the neutrally linearly stable asynchronous regime. The latter has a finite life time for finite ensembles, this time grows with the ensemble size as a power law. (C) 2014 Elsevier B.V. All rights reserved.},
  language  = {en}
}