arXiv subjects

Arkady Pikovsky

Publications and source records attributed to Arkady Pikovsky.

At least 55 records · Page 3Linked to original sources

arXiv2020

Solitary phase waves in a chain of autonomous oscillators

In the present paper we study phase waves of self-sustained oscillators with a nearest neighbor dispersive coupling on an infinite lattice. To analyze the underlying dynamics we approximate the lattice with a quasi-continuum, QC. The resulting partial differential model is then further reduced to the Gardner equation which predicts many properties of the underlying solitary structures. Using an iterative procedure on the original lattice equations we determine the shapes of solitary waves, kinks, and the flat-like solitons, that we refer to as flatons. Direct numerical experiments reveal that the interaction of solitons and flatons on the lattice is notably clean. All in all we find that both the QC and the Gardner equation predict remarkably well the discrete patterns and their dynamics.

nlin.PS↗

arXiv2019

Locking and regularisation of chimeras by periodic forcing

We study how a chimera state in a one-dimensional medium of non-locally coupled oscillators responses to a periodic external force. On a macroscopic level, where chimera can be considered as an oscillating object, forcing leads to entrainment of the chimera's frequency inside an Arnold tongue. On a mesoscopic level, where chimera can be viewed as a inhomogeneous, stationary or nonstationary pattern, strong forcing can lead to reguralization of an unstationary chimera. On a microscopic level of the dynamics of individual oscillators, forcing outside of the Arnold tongue leads to a multi-plateu state with nontrivial locking properties.

nlin.PS↗

arXiv2019

Blinking chimeras in globally coupled rotators

In globally coupled ensembles of identical oscillators so-called chimera states can be observed. The chimera state is a symmetry-broken regime, where a subset of oscillators forms a cluster, a synchronized population, while the rest of the system remains a collection of non-synchronized, scattered units. We describe here a blinking chimera regime in an ensemble of seven globally coupled rotators (Kuramoto oscillators with inertia). It is characterized by a death-birth process, where a long-term stable cluster of four oscillators suddenly dissolves and is very quickly reborn with a new, reshuffled configuration. We identify three different kinds of rare blinking events and give a quantitative characterization by applying stability analysis to the long-lived chaotic state and to the short-lived regular regimes which arise when the cluster dissolves.

nlin.CD↗

arXiv2019

Stabilization of direct numerical simulation for finite truncations of circular cumulant expansions

We study a numerical instability of direct simulations with truncated equation chains for the "circular cumulant" representation and two approaches to its suppression. The approaches are tested for a chimera-bearing hierarchical population of coupled oscillators. The stabilization techniques can be efficiently applied without significant effect on the natural system dynamics within a finite vicinity of the Ott-Antonsen manifold for direct numerical simulations with up to 20 cumulants; with increasing deviation from the Ott-Antonsen manifold the stabilization becomes more problematic.

cond-mat.stat-mech↗

arXiv2019

Repulsively Coupled Kuramoto-Sakaguchi Phase Oscillators Ensemble Subject to Common Noise

We consider the Kuramoto-Sakaguchi model of identical coupled phase oscillators with a common noisy forcing. While common noise always tends to synchronize the oscillators, a strong repulsive coupling prevents the fully synchronous state and leads to a nontrivial distribution of oscillator phases. In previous numerical simulations, a formation of stable multicluster states has been observed in this regime. However we argue here, that because identical phase oscillators in the Kuramoto-Sakaguchi model form a partially integrable system according to the Watanabe-Strogatz theory, the formation of clusters is impossible. Integrating with various time steps reveals that clustering is a numerical artifact, explained by the existence of higher order Fourier terms in the errors of the employed numerical integration schemes. Monitoring the induced change in certain integrals of motion we quantify these errors. We support these observations by showing, on the basis of the analysis of the corresponding Fokker-Planck equation, that two-cluster states are non-attractive. On the other hand, in ensembles of general limit cycle oscillators, such as Van der Pol oscillators, due to an anharmonic phase response function, as well as additional amplitude dynamics, multiclusters can occur naturally.

cond-mat.stat-mech↗

arXiv2019

Synchrony breakdown and noise-induced oscillation death in ensembles of serially connected spin-torque oscillators

We consider collective dynamics in the ensemble of serially connected spin-torque oscillators governed by the Landau-Lifshitz-Gilbert-Slonczewski magnetization equation. Proximity to homoclinicity hampers synchronization of spin-torque oscillators: when the synchronous ensemble experiences the homoclinic bifurcation, the Floquet multiplier, responsible for the temporal evolution of small deviations from the ensemble mean, diverges. Depending on the configuration of the contour, sufficiently strong common noise, exemplified by stochastic oscillations of the current through the circuit, may suppress precession of the magnetic field for all oscillators. We derive the explicit expression for the threshold amplitude of noise, enabling this suppression.

nlin.CD↗

arXiv2019

Stochastic bursting in unidirectionally delay-coupled noisy excitable systems

We show that \emph{stochastic bursting} is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation, i.e., when the time delays in each connection are much larger than the characteristic duration of the spikes, the observed rather coherent spike pattern can be described by idealized coupled point processes with a leader-follower relationship. We derive analytically the statistics of the spikes in each unit, pairwise correlations between any two units, and the spectrum of the total output from the network. Theory is in a good agreement with the simulations with a network of theta-neurons.

cond-mat.dis-nn↗

arXiv2019

Phase demodulation with iterative Hilbert transform embeddings

We propose an efficient method for demodulation of phase modulated signals via iterated Hilbert transform embeddings. We show that while a usual approach based on one application of the Hilbert transform provides only an approximation to a proper phase, with iterations the accuracy is essentially improved, up to precision limited mainly by the discretization effects. We demonstrate that the method is applicable to arbitrarily complex waveforms, and to modulations fast compared to the basic frequency. Furthermore, we develop a perturbative theory applicable to simple cosine waveforms, showing convergence of the technique.

physics.comp-ph↗

arXiv2018

Numerical phase reduction beyond the first order approximation

We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for the evolution of the phase. Our simulations demonstrate that the description of the dynamics solely by phase variables can be valid for rather strong coupling strengths and large deviations from the limit cycle. Coupling functions depend crucially on the coupling and are generally non-decomposable in phase response and forcing terms. We also discuss limitations of the approach.

physics.comp-ph↗

arXiv2018

Describing dynamics of driven multistable oscillators with phase transfer curves

Phase response curve is an important tool in studies of stable self-sustained oscillations; it describes a phase shift under action of an external perturbation. We consider multistable oscillators with several stable limit cycles. Under a perturbation, transitions from one oscillating mode to another one may occur. We define phase transfer curves to describe the phase shifts at such transitions. This allows for a construction of one-dimensional maps that characterize periodically kicked multistable oscillators. We show, that these maps are good approximations of the full dynamics for large periods of forcing.

nlin.CD↗

arXiv2018

Delay-induced stochastic bursting in excitable noisy systems

We show that a cumulative action of noise and delayed feedback on an excitable theta-neuron leads to rather coherent stochastic bursting. An idealized point process, valid if the characteristic time scales in the problem are well-separated, is used to describe statistical properties such as the power spectrum and the interspike interval distribution. We show how the main parameters of the point process, the spontaneous excitation rate and the probability to induce a spike during the delay action, can be calculated from the solutions of a stationary and a forced Fokker-Planck equation.

cond-mat.stat-mech↗

arXiv2018

Collective mode reductions for populations of coupled noisy oscillators

We analyze 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 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.

nlin.AO↗

arXiv2018

Unraveling the Chaos-land and its organization in the Rabinovich System

A suite of analytical and computational techniques based on symbolic representations of simple and complex dynamics, is further developed and employed to unravel the global organization of bi-parametric structures that underlie the emergence of chaos in a simplified resonantly coupled wave triplet system, known as the Rabinovich system. Bi-parametric scans reveal the stunning intricacy and intramural connections between homoclinic and heteroclinic connections, and codimension-2 Bykov T-points and saddle structures, which are the prime organizing centers of complexity of the bifurcation unfolding of the given system. This suite includes Deterministic Chaos Prospector (DCP) to sweep and effectively identify regions of simple (Morse-Smale) and chaotic structurally unstable dynamics in the system. Our analysis provides striking new insights into the complex behaviors exhibited by this and similar systems.

nlin.CD↗

arXiv2018

Dynamics of noisy oscillator populations beyond the Ott-Antonsen ansatz

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 the 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.

nlin.AO↗

arXiv2018

Transition to Collective Oscillations in Finite Kuramoto Ensembles

We present an alternative approach to finite-size effects around the synchronization transition in the standard Kuramoto model. Our main focus lies on the conditions under which a collective oscillatory mode is well defined. For this purpose, the minimal value of the amplitude of the complex Kuramoto order parameter appears as a proper indicator. The dependence of this minimum on coupling strength varies due to sampling variations and correlates with the sample kurtosis of the natural frequency distribution. The skewness of the frequency sample determines the frequency of the resulting collective mode. The effects of kurtosis and skewness hold in the thermodynamic limit of infinite ensembles. We prove this by integrating a self-consistency equation for the complex Kuramoto order parameter for two families of distributions with controlled kurtosis and skewness, respectively.

nlin.AO↗

arXiv2018

Disentangling Respiratory Sinus Arrhythmia in Heart Rate Variability Records

Different measures of heart rate variability and particularly of respiratory sinus arrhythmia are widely used in research and clinical applications. Inspired by the ideas from the theory of coupled oscillators, we use simultaneous measurements of respiratory and cardiac activity to perform a nonlinear decomposition of the heart rate variability into the respiratory-related component and the rest. We suggest to exploit the technique as a universal preprocessing tool, both for the analysis of respiratory influence on the heart rate as well as in cases when effects of other factors on the heart rate variability are in focus. The theoretical consideration is illustrated by the analysis of 25 data sets from healthy subjects.

physics.med-ph↗

arXiv2017

Synchronization of coupled active rotators by common noise

We study the effect of common noise on coupled active rotators. While such a noise always facilitates synchrony, coupling may be attractive or repulsing. We develop an analytical approach based on a transformation to approximate angle-action variables and averaging over fast rotations. For identical rotators, we describe a transition from full to partial synchrony at a critical value of repulsive coupling. For nonidentical rotators, the most nontrivial effect occurs at moderate repulsive coupling, where a juxtaposition of phase locking with frequency repulsion (anti-entrainment) is observed. We show that the frequency repulsion obeys a nontrivial power law.

cond-mat.stat-mech↗

arXiv2017

Dynamics of oscillators globally coupled via two mean fields

Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean fields. We derive stability properties of the incoherent state and find traveling wave solutions with different locking patterns; stability properties of these waves are found numerically. Mostly nontrivial states appear when the two fields compete, i.e. one tends to synchronize oscillators while the other one desynchronizes them. Here we identify normal branches which bifurcate from the incoherent state in a usual way, and anomalous branches, appearance of which cannot be described as a bifurcation. Furthermore, hybrid branches combining properties of both are described. In the situations where no stable traveling wave exists, modulated quasiperiodic in time dynamics is observed. Our results indicate that a competition between two coupling channels can lead to a complex system behavior, providing a potential generalized framework for understanding of complex phenomena in natural oscillatory systems.

nlin.CD↗