TY  - JOUR
A1  - Nagornov, Roman
A1  - Osipoy, Grigory
A1  - Komarov, Maxim
A1  - Pikovskij, Arkadij
A1  - Shilnikov, Andrey
T1  - Mixed-mode synchronization between two inhibitory neurons with post-inhibitory rebound
JF  - Communications in nonlinear science & numerical simulation
N2  - 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.
KW  - Synchronization
KW  - Hodgkin-Huxley model
KW  - Half-center oscillator
KW  - Post-inhibitory rebound
Y1  - 2016
U6  - https://doi.org/10.1016/j.cnsns.2015.11.024
SN  - 1007-5704
SN  - 1878-7274
VL  - 36
SP  - 175
EP  - 191
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Komarov, Maxim
A1  - Pikovskij, Arkadij
T1  - The Kuramoto model of coupled oscillators with a bi-harmonic coupling function
JF  - Physica : D, Nonlinear phenomena
N2  - 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.
KW  - Kuramoto model
KW  - Bi-harmonic coupling function
KW  - Multi-branch entrainment
KW  - Synchronization
Y1  - 2014
U6  - https://doi.org/10.1016/j.physd.2014.09.002
SN  - 0167-2789
SN  - 1872-8022
VL  - 289
SP  - 18
EP  - 31
PB  - Elsevier
CY  - Amsterdam
ER  -