TY - JOUR A1 - Levnajic, Zoran A1 - Pikovskij, Arkadij T1 - Untangling complex dynamical systems via derivative-variable correlations JF - Scientific reports N2 - Inferring the internal interaction patterns of a complex dynamical system is a challenging problem. Traditional methods often rely on examining the correlations among the dynamical units. However, in systems such as transcription networks, one unit's variable is also correlated with the rate of change of another unit's variable. Inspired by this, we introduce the concept of derivative-variable correlation, and use it to design a new method of reconstructing complex systems (networks) from dynamical time series. Using a tunable observable as a parameter, the reconstruction of any system with known interaction functions is formulated via a simple matrix equation. We suggest a procedure aimed at optimizing the reconstruction from the time series of length comparable to the characteristic dynamical time scale. Our method also provides a reliable precision estimate. We illustrate the method's implementation via elementary dynamical models, and demonstrate its robustness to both model error and observation error. Y1 - 2014 U6 - https://doi.org/10.1038/srep05030 SN - 2045-2322 VL - 4 PB - Nature Publ. Group CY - London 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 - TY - JOUR A1 - Komarov, Maxim A1 - Gupta, Shamik A1 - Pikovskij, Arkadij T1 - Synchronization transitions in globally coupled rotors in the presence of noise and inertia: Exact results JF - epl : a letters journal exploring the frontiers of physics N2 - 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 Y1 - 2014 U6 - https://doi.org/10.1209/0295-5075/106/40003 SN - 0295-5075 SN - 1286-4854 VL - 106 IS - 4 PB - EDP Sciences CY - Mulhouse ER - TY - JOUR A1 - Vlasov, Vladimir A1 - Macau, Elbert E. N. A1 - Pikovskij, Arkadij T1 - Synchronization of oscillators in a Kuramoto-type model with generic coupling JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of oscillators to the mean field and to different forces from the mean field on oscillators. We present the explicit solutions of self-consistency equations for the amplitude and frequency of the mean field in a parametric form, valid for noise-free and noise-driven oscillators. As an example, we consider spatially spreaded oscillators for which the coupling properties are determined by finite velocity of signal propagation. (C) 2014 AIP Publishing LLC. Y1 - 2014 U6 - https://doi.org/10.1063/1.4880835 SN - 1054-1500 SN - 1089-7682 VL - 24 IS - 2 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Kralemann, Bjoern A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael T1 - Reconstructing effective phase connectivity of oscillator networks from observations JF - New journal of physics : the open-access journal for physics N2 - We present a novel approach for recovery of the directional connectivity of a small oscillator network by means of the phase dynamics reconstruction from multivariate time series data. The main idea is to use a triplet analysis instead of the traditional pairwise one. Our technique reveals an effective phase connectivity which is generally not equivalent to a structural one. We demonstrate that by comparing the coupling functions from all possible triplets of oscillators, we are able to achieve in the reconstruction a good separation between existing and non-existing connections, and thus reliably reproduce the network structure. KW - network reconstruction KW - coupled oscillators KW - connectivity KW - data analysis Y1 - 2014 U6 - https://doi.org/10.1088/1367-2630/16/8/085013 SN - 1367-2630 VL - 16 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Kralemann, Bjoern A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael T1 - Reconstructing connectivity of oscillator networks from multimodal observations JF - Biomedizinische Technik = Biomedical engineering Y1 - 2014 U6 - https://doi.org/10.1515/bmt-2014-4089 SN - 0013-5585 SN - 1862-278X VL - 59 SP - S220 EP - S220 PB - De Gruyter CY - Berlin ER - TY - JOUR A1 - Lepri, Stefano A1 - Pikovskij, Arkadij T1 - Nonreciprocal wave scattering on nonlinear string-coupled oscillators JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a "chaotic diode," where transmission is periodic in one direction and chaotic in the opposite one, is reported. (C) 2014 AIP Publishing LLC. Y1 - 2014 U6 - https://doi.org/10.1063/1.4899205 SN - 1054-1500 SN - 1089-7682 VL - 24 IS - 4 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Pollatos, Olga A1 - Yeldesbay, Azamat A1 - Pikovskij, Arkadij A1 - Rosenblum, Michael T1 - How much time has passed? Ask your heart JF - Frontiers in neurorobotics N2 - Internal signals like one's heartbeats are centrally processed via specific pathways and both their neural representations as well as their conscious perception (interoception) provide key information for many cognitive processes. Recent empirical findings propose that neural processes in the insular cortex, which are related to bodily signals, might constitute a neurophysiological mechanism for the encoding of duration. Nevertheless, the exact nature of such a proposed relationship remains unclear. We aimed to address this question by searching for the effects of cardiac rhythm on time perception by the use of a duration reproduction paradigm. Time intervals used were of 0.5, 2, 3, 7, 10, 14, 25, and 40s length. In a framework of synchronization hypothesis, measures of phase locking between the cardiac cycle and start/stop signals of the reproduction task were calculated to quantify this relationship. The main result is that marginally significant synchronization indices (Sls) between the heart cycle and the time reproduction responses for the time intervals of 2, 3, 10, 14, and 25s length were obtained, while results were not significant for durations of 0.5, 7, and 40s length. On the single participant level, several subjects exhibited some synchrony between the heart cycle and the time reproduction responses, most pronounced for the time interval of 25s (8 out of 23 participants for 20% quantile). Better time reproduction accuracy was not related with larger degree of phase locking, but with greater vagal control of the heart. A higher interoceptive sensitivity (IS) was associated with a higher synchronization index (SI) for the 2s time interval only. We conclude that information obtained from the cardiac cycle is relevant for the encoding and reproduction of time in the time span of 2-25s. Sympathovagal tone as well as interoceptive processes mediate the accuracy of time estimation. KW - time interval reproduction KW - synchronization KW - heart cycle KW - interoception KW - interoceptive sensitivity Y1 - 2014 U6 - https://doi.org/10.3389/fnbot.2014.00015 SN - 1662-5218 VL - 8 SP - 1 EP - 9 PB - Frontiers Research Foundation CY - Lausanne ER - TY - JOUR A1 - Pikovskij, Arkadij A1 - Gupta, Shamik A1 - Teles, Tarcisio N. A1 - Benetti, Fernanda P. C. A1 - Pakter, Renato A1 - Levin, Yan A1 - Ruffo, Stefano T1 - Ensemble inequivalence in a mean-field XY model with ferromagnetic and nematic couplings JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We explore ensemble inequivalence in long-range interacting systems by studying an XY model of classical spinswith ferromagnetic and nematic coupling. We demonstrate the inequivalence bymapping themicrocanonical phase diagram onto the canonical one, and also by doing the inverse mapping. We show that the equilibrium phase diagrams within the two ensembles strongly disagree within the regions of first-order transitions, exhibiting interesting features like temperature jumps. In particular, we discuss the coexistence and forbidden regions of different macroscopic states in both the phase diagrams. Y1 - 2014 U6 - https://doi.org/10.1103/PhysRevE.90.062141 SN - 1539-3755 SN - 1550-2376 VL - 90 IS - 6 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Levanova, T. A. A1 - Osipov, Grigory V. A1 - Pikovskij, Arkadij T1 - Coherence properties of cycling chaos JF - Communications in nonlinear science & numerical simulation N2 - Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switchings between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering nearly periodic regimes that appear close to the cycling chaos due to imperfections or to instability. Using numerical simulations of coupled Lorenz, Roessler, and logistic map models, we show that the coherence is high in the case of imperfection (so that asymptotically the cycling chaos is very regular), while it is low close to instability of the cycling chaos. (C) 2014 Elsevier B. V. All rights reserved. KW - Heteroclinic cycle KW - Chaos KW - Coherence Y1 - 2014 U6 - https://doi.org/10.1016/j.cnsns.2014.01.011 SN - 1007-5704 SN - 1878-7274 VL - 19 IS - 8 SP - 2734 EP - 2739 PB - Elsevier CY - Amsterdam ER -