TY - JOUR A1 - Bolotov, M. I. A1 - Osipov, Grigory V. A1 - Pikovskij, Arkadij T1 - Marginal chimera state at cross-frequency locking of pulse-coupled neural networks JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We consider two coupled populations of leaky integrate-and-fire neurons. Depending on the coupling strength, mean fields generated by these populations can have incommensurate frequencies or become frequency locked. In the observed 2:1 locking state of the mean fields, individual neurons in one population are asynchronous with the mean fields, while in another population they have the same frequency as the mean field. These synchronous neurons form a chimera state, where part of them build a fully synchronized cluster, while other remain scattered. We explain this chimera as a marginal one, caused by a self-organized neutral dynamics of the effective circle map. Y1 - 2016 U6 - https://doi.org/10.1103/PhysRevE.93.032202 SN - 2470-0045 SN - 2470-0053 VL - 93 PB - American Physical Society CY - College Park ER - 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 - Pikovskij, Arkadij T1 - Reconstruction of a neural network from a time series of firing rates JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Randomly coupled neural fields demonstrate irregular variation of firing rates, if the coupling is strong enough, as has been shown by Sompolinsky et al. [Phys. Rev. Lett. 61, 259 (1988)]. We present a method for reconstruction of the coupling matrix from a time series of irregular firing rates. The approach is based on the particular property of the nonlinearity in the coupling, as the latter is determined by a sigmoidal gain function. We demonstrate that for a large enough data set and a small measurement noise, the method gives an accurate estimation of the coupling matrix and of other parameters of the system, including the gain function. Y1 - 2016 U6 - https://doi.org/10.1103/PhysRevE.93.062313 SN - 2470-0045 SN - 2470-0053 VL - 93 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Pimenova, Anastasiya V. A1 - Goldobin, Denis S. A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij T1 - Interplay of coupling and common noise at the transition to synchrony in oscillator populations JF - Scientific reports N2 - There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony, and we focus on this nontrivial situation. For identical oscillators, the fully synchronous state remains stable for small repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion (instead of usual convergence) of the oscillators frequencies at synchrony; the latter effect disappears if noise vanishes. Y1 - 2016 U6 - https://doi.org/10.1038/srep38518 SN - 2045-2322 VL - 6 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Vlasov, Vladimir A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij T1 - Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe-Strogatz integrability JF - Journal of physics : A, Mathematical and theoretical N2 - As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations. KW - Kuramoto model KW - oscillator populations KW - integrability KW - perturbation theory Y1 - 2016 U6 - https://doi.org/10.1088/1751-8113/49/31/31LT02 SN - 1751-8113 SN - 1751-8121 VL - 49 PB - IOP Publ. Ltd. CY - Bristol ER -