@article{KomarovBazhenov2016, author = {Komarov, Maxim and Bazhenov, Maxim}, title = {Linking dynamics of the inhibitory network to the input structure}, series = {Journal of computational neuroscience}, volume = {41}, journal = {Journal of computational neuroscience}, publisher = {Springer}, address = {Dordrecht}, issn = {0929-5313}, doi = {10.1007/s10827-016-0622-8}, pages = {367 -- 391}, year = {2016}, language = {en} } @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{KomarovPikovskij2013, author = {Komarov, Maxim and Pikovskij, Arkadij}, title = {Multiplicity of singular synchronous States in the kuramoto model of coupled oscillators}, series = {Physical review letters}, volume = {111}, journal = {Physical review letters}, number = {20}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.111.204101}, pages = {5}, year = {2013}, abstract = {We study the Kuramoto model of globally coupled oscillators with a biharmonic coupling function. We develop an analytic self-consistency approach to find stationary synchronous states in the thermodynamic limit and demonstrate that there is a huge multiplicity of such states, which differ microscopically in the distributions of locked phases. These synchronous regimes already exist prior to the linear instability transition of the fully asynchronous state. In the presence of white Gaussian noise, the multiplicity is lifted, but the dependence of the order parameters on coupling constants remains nontrivial.}, language = {en} } @article{KomarovPikovskij2013, author = {Komarov, Maxim and Pikovskij, Arkadij}, title = {Dynamics of multifrequency oscillator communities}, series = {Physical review letters}, volume = {110}, journal = {Physical review letters}, number = {13}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.110.134101}, pages = {5}, year = {2013}, abstract = {We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between the communities' frequencies are derived. The simplest situation of three resonantly interacting groups is analyzed in detail. We find conditions for the mutual coupling to promote or suppress synchrony in individual populations and present examples where the interaction between communities leads to their synchrony or to a partially asynchronous state or to a chaotic dynamics of order parameters. DOI: 10.1103/PhysRevLett.110.134101}, language = {en} } @article{KomarovPikovskij2011, author = {Komarov, Maxim and Pikovskij, Arkadij}, title = {Effects of nonresonant interaction in ensembles of phase 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.84.016210}, pages = {12}, year = {2011}, abstract = {We consider general properties of groups of interacting oscillators, for which the natural frequencies are not in resonance. Such groups interact via nonoscillating collective variables like the amplitudes of the order parameters defined for each group. We treat the phase dynamics of the groups using the Ott-Antonsen ansatz and reduce it to a system of coupled equations for the order parameters. We describe different regimes of cosynchrony in the groups. For a large number of groups, heteroclinic cycles, corresponding to a sequential synchronous activity of groups and chaotic states where the order parameters oscillate irregularly, are possible.}, 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} } @article{KomarovGuptaPikovskij2014, author = {Komarov, Maxim and Gupta, Shamik and Pikovskij, Arkadij}, title = {Synchronization transitions in globally coupled rotors in the presence of noise and inertia: Exact results}, series = {epl : a letters journal exploring the frontiers of physics}, volume = {106}, journal = {epl : a letters journal exploring the frontiers of physics}, number = {4}, publisher = {EDP Sciences}, address = {Mulhouse}, issn = {0295-5075}, doi = {10.1209/0295-5075/106/40003}, pages = {6}, year = {2014}, abstract = {We study a generic model of globally coupled rotors that includes the effects of noise, phase shift in the coupling, and distributions of moments of inertia and natural frequencies of oscillation. As particular cases, the setup includes previously studied Sakaguchi-Kuramoto, Hamiltonian and Brownian mean-field, and Tanaka-Lichtenberg-Oishi and Acebron-Bonilla-Spigler models. We derive an exact solution of the self-consistent equations for the order parameter in the stationary state, valid for arbitrary parameters in the dynamics, and demonstrate nontrivial phase transitions to synchrony that include reentrant synchronous regimes. Copyright (C) EPLA, 2014}, language = {en} } @article{KomarovPikovskij2015, author = {Komarov, Maxim and Pikovskij, Arkadij}, title = {Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {92}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.92.020901}, pages = {5}, year = {2015}, abstract = {We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles and disappears in the thermodynamic limit. For all considered setups, which include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.}, language = {en} } @article{VlasovKomarovPikovskij2015, author = {Vlasov, Vladimir and Komarov, Maxim and Pikovskij, Arkadij}, title = {Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {48}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {10}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8113/48/10/105101}, pages = {16}, year = {2015}, abstract = {We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder-diversity of the intrinsic oscillators' frequencies, and external independent noise forces. Based on the self-consistent formulation, we derive analytic solutions for different synchronous states. We report on various non-trivial transitions from incoherence to synchrony, with the following possible scenarios: simple supercritical transition (similar to classical Kuramoto model); subcritical transition with large area of bistability of incoherent and synchronous solutions; appearance of a symmetric two-cluster solution which can coexist with the regular synchronous state. We show that the interplay between relatively small white noise and finite-size fluctuations can lead to metastability of the asynchronous solution.}, language = {en} } @article{KomarovPikovskij2015, author = {Komarov, Maxim and Pikovskij, Arkadij}, title = {Intercommunity resonances in multifrequency ensembles of coupled oscillators}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {92}, 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.92.012906}, pages = {11}, year = {2015}, abstract = {We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to the resonance 2 : 1 is considered in detail. We construct uniformly rotating solutions describing synchronization inside communities and between them. Remarkably, cross coupling across the frequencies can promote synchrony even when ensembles are separately asynchronous. We also show that the transition to synchrony due to the cross coupling is accompanied by a huge multiplicity of distinct synchronous solutions, which is directly related to a multibranch entrainment. On the other hand, for synchronous populations, the cross-frequency coupling can destroy phase locking and lead to chaos of mean fields.}, language = {en} }