@article{TyulkinaGoldobinKlimenkoetal.2019, author = {Tyulkina, Irina V. and Goldobin, Denis S. and Klimenko, Lyudmila S. and Pikovskij, Arkadij}, title = {Two-Bunch Solutions for the Dynamics of Ott-Antonsen Phase Ensembles}, series = {Radiophysics and Quantum Electronics}, volume = {61}, journal = {Radiophysics and Quantum Electronics}, number = {8-9}, publisher = {Springer}, address = {New York}, issn = {0033-8443}, doi = {10.1007/s11141-019-09924-7}, pages = {640 -- 649}, year = {2019}, abstract = {We have developed a method for deriving systems of closed equations for the dynamics of order parameters in the ensembles of phase oscillators. The Ott-Antonsen equation for the complex order parameter is a particular case of such equations. The simplest nontrivial extension of the Ott-Antonsen equation corresponds to two-bunch states of the ensemble. Based on the equations obtained, we study the dynamics of multi-bunch chimera states in coupled Kuramoto-Sakaguchi ensembles. We show an increase in the dimensionality of the system dynamics for two-bunch chimeras in the case of identical phase elements and a transition to one-bunch "Abrams chimeras" for imperfect identity (in the latter case, the one-bunch chimeras become attractive).}, language = {en} } @article{TyulkinaGoldobinKlimenkoetal.2018, author = {Tyulkina, Irina and Goldobin, Denis S. and Klimenko, Lyudmila S. and Pikovskij, Arkadij}, title = {Dynamics of noisy oscillator populations beyond the Ott-Antonsen Ansatz}, series = {Physical review letters}, volume = {120}, journal = {Physical review letters}, number = {26}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.120.264101}, pages = {6}, year = {2018}, abstract = {We develop an approach for the description of the dynamics of large populations of phase oscillators based on "circular cumulants" instead of the Kuramoto-Daido order parameters. In the thermodynamic limit, these variables yield a simple representation of the Ott-Antonsen invariant solution [E. Ott and T. M. Antonsen, Chaos 18, 037113 (2008)] and appear appropriate for constructing perturbation theory on top of the Ott-Antonsen ansatz. We employ this approach to study the impact of small intrinsic noise on the dynamics. As a result, a closed system of equations for the two leading cumulants, describing the dynamics of noisy ensembles, is derived. We exemplify the general theory by presenting the effect of noise on the Kuramoto system and on a chimera state in two symmetrically coupled populations.}, language = {en} } @misc{PimenovaGoldobinRosenblumetal.2016, author = {Pimenova, Anastasiya V. and Goldobin, Denis S. and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Interplay of coupling and common noise at the transition to synchrony in oscillator populations}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-103471}, pages = {7}, year = {2016}, abstract = {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.}, language = {en} } @article{PimenovaGoldobinRosenblumetal.2016, author = {Pimenova, Anastasiya V. and Goldobin, Denis S. and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Interplay of coupling and common noise at the transition to synchrony in oscillator populations}, series = {Scientific reports}, volume = {6}, journal = {Scientific reports}, publisher = {Nature Publ. Group}, address = {London}, issn = {2045-2322}, doi = {10.1038/srep38518}, pages = {7}, year = {2016}, abstract = {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.}, language = {en} } @article{PikovskijDolmatovaGoldobin2019, author = {Pikovskij, Arkadij and Dolmatova, A. and Goldobin, Denis S.}, title = {Correlations of the States of Non-Entrained Oscillators in the Kuramoto Ensemble with Noise in the Mean Field}, series = {Radiophysics and Quantum Electronics}, volume = {61}, journal = {Radiophysics and Quantum Electronics}, number = {8-9}, publisher = {Springer}, address = {New York}, issn = {0033-8443}, doi = {10.1007/s11141-019-09927-4}, pages = {672 -- 680}, year = {2019}, abstract = {We consider the dynamics of the Kuramoto ensemble oscillators not included in a common synchronized cluster, where the mean field is subject to fluctuations. The fluctuations can be either related to the finite size of the ensemble or superimposed on the mean field in the form of common noise due to the constructive features of the system. It is shown that the states of such oscillators with close natural frequencies appear correlated with each other, since the mean-field fluctuations act as common noise. We quantify the effect with the synchronization index of two oscillators, which is calculated numerically and analytically as a function of the frequency difference and noise intensity. The results are rigorous for large ensembles with additional noise superimposed on the mean field and are qualitatively true for the systems where the mean-field fluctuations are due to the finite size of the ensemble. In the latter case, the effect is found to be independent of the number of oscillators in the ensemble.}, language = {en} } @article{GoldobinZaikin2009, author = {Goldobin, Denis S. and Zaikin, Alexey}, title = {Towards quantitative prediction of proteasomal digestion patterns of proteins}, issn = {1742-5468}, doi = {10.1088/1742-5468/2009/01/P01009}, year = {2009}, abstract = {We discuss the problem of proteasomal degradation of proteins. Though proteasomes are important for all aspects of cellular metabolism, some details of the physical mechanism of the process remain unknown. We introduce a stochastic model of the proteasomal degradation of proteins, which accounts for the protein translocation and the topology of the positioning of cleavage centers of a proteasome from first principles. For this model we develop a mathematical description based on a master equation and techniques for reconstruction of the cleavage specificity inherent to proteins and the proteasomal translocation rates, which are a property of the proteasome species, from mass spectroscopy data on digestion patterns. With these properties determined, one can quantitatively predict digestion patterns for new experimental set-ups. Additionally we design an experimental set-up for a synthetic polypeptide with a periodic sequence of amino acids, which enables especially reliable determination of translocation rates.}, language = {en} } @article{GoldobinTyulkinaKlimenkoetal.2018, author = {Goldobin, Denis S. and Tyulkina, Irina V. and Klimenko, Lyudmila S. and Pikovskij, Arkadij}, title = {Collective mode reductions for populations of coupled noisy oscillators}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {28}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {10}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5053576}, pages = {6}, year = {2018}, abstract = {We analyze the accuracy of different low-dimensional reductions of the collective dynamics in large populations of coupled phase oscillators with intrinsic noise. Three approximations are considered: (i) the Ott-Antonsen ansatz, (ii) the Gaussian ansatz, and (iii) a two-cumulant truncation of the circular cumulant representation of the original system's dynamics. For the latter, we suggest a closure, which makes the truncation, for small noise, a rigorous first-order correction to the Ott-Antonsen ansatz, and simultaneously is a generalization of the Gaussian ansatz. The Kuramoto model with intrinsic noise and the population of identical noisy active rotators in excitable states with the Kuramoto-type coupling are considered as examples to test the validity of these approximations. For all considered cases, the Gaussian ansatz is found to be more accurate than the Ott-Antonsen one for high-synchrony states only. The two-cumulant approximation is always superior to both other approximations. Synchrony of large ensembles of coupled elements can be characterised by the order parameters—the mean fields. Quite often, the evolution of these collective variables is surprisingly simple, which makes a description with only a few order parameters feasible. Thus, one tries to construct accurate closed low-dimensional mathematical models for the dynamics of the first few order parameters. These models represent useful tools for gaining insight into the underlaying mechanisms of some more sophisticated collective phenomena: for example, one describes coupled populations by virtue of coupled equations for the relevant order parameters. A regular approach to the construction of closed low-dimensional systems is also beneficial for dealing with phenomena, which are beyond the applicability scope of these models; for instance, with such an approach, one can determine constraints on clustering in populations. There are two prominent types of situations, where the low-dimensional models can be constructed: (i) for a certain class of ideal paradigmatic systems of coupled phase oscillators, the Ott-Antonsen ansatz yields an exact equation for the main order parameter and (ii) the Gaussian approximation for the probability density of the phases, also yielding a low-dimensional closure, is frequently quite accurate. In this paper, we compare applications of these two model reductions for situations, where neither of them is perfectly accurate. Furthermore, we construct a new reduction approach which practically works as a first-order correction to the best of the two basic approximations.}, language = {en} } @article{GoldobinShklyaeva2009, author = {Goldobin, Denis S. and Shklyaeva, Elizaveta V.}, title = {Diffusion of a passive scalar by convective flows under parametric disorder}, issn = {1742-5468}, doi = {10.1088/1742-5468/2009/01/P01024}, year = {2009}, abstract = {We study transport of a weakly diffusive pollutant (a passive scalar) through thermoconvective flow in a fluid- saturated horizontal porous layer heated from below under frozen parametric disorder. In the presence of disorder (random frozen inhomogeneities of the heating or of macroscopic properties of the porous matrix), spatially localized flow patterns appear below the convective instability threshold of the system without disorder. Thermoconvective. ows crucially affect the transport of a pollutant along the layer, especially when its molecular diffusion is weak. The effective (or eddy) diffusivity also allows us to observe the transition from a set of localized currents to an almost everywhere intense 'global' flow. We present results of numerical calculation of the effective diffusivity and discuss them in the context of localization of fluid currents and the transition to a 'global' flow. Our numerical findings are in good agreement with the analytical theory that we develop for the limit of a small molecular diffusivity and sparse domains of localized currents. Though the results are obtained for a specific physical system, they are relevant for a broad variety of fluid dynamical systems.}, language = {en} } @article{GoldobinPimenovaRosenblumetal.2017, author = {Goldobin, Denis S. and Pimenova, Anastasiya V. and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Competing influence of common noise and desynchronizing coupling on synchronization in the Kuramoto-Sakaguchi ensemble}, series = {European physical journal special topics}, volume = {226}, journal = {European physical journal special topics}, publisher = {Springer}, address = {Heidelberg}, issn = {1951-6355}, doi = {10.1140/epjst/e2017-70039-y}, pages = {1921 -- 1937}, year = {2017}, abstract = {We describe analytically synchronization and desynchronization effects in an ensemble of phase oscillators driven by common noise and by global coupling. Adopting the Ott-Antonsen ansatz, we reduce the dynamics to closed stochastic equations for the order parameters, and study these equations for the cases of populations of identical and nonidentical oscillators. For nonidentical oscillators we demonstrate a counterintuitive effect of divergence of individual frequencies for moderate repulsive coupling, while the order parameter remains large.}, language = {en} } @article{GoldobinPikovskij2006, author = {Goldobin, Denis S. and Pikovskij, Arkadij}, title = {Antireliability of noise-driven neurons}, issn = {1539-3755}, doi = {10.1103/Physreve.73.061906}, year = {2006}, abstract = {We demonstrate, within the framework of the FitzHugh-Nagumo model, that a firing neuron can respond to a noisy driving in a nonreliable manner: the same Gaussian white noise acting on identical neurons evokes different patterns of spikes. The effect is characterized via calculations of the Lyapunov exponent and the event synchronization correlations. We construct a theory that explains the antireliability as a combined effect of a high sensitivity to noise of some stages of the dynamics and nonisochronicity of oscillations. Geometrically, the antireliability is described by a random noninvertible one-dimensional map}, language = {en} }